Lines And Angles - Class 7 Maths - Extra Questions

In Fig., lines AB and CD are parallel and P is any point as shown in the figure. Show that $$\angle ABP+\angle CDP= \angle DPB$$.
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In figure, write another name for $$\angle 2$$.
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Find $$x$$ and $$y$$.
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In the adjoining figure, name the following pairs of angles.
Obstuse vertically opposite angles 

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In the given figure three lines $$\overleftrightarrow{AB}, \overleftrightarrow{CD}$$ and $$\overleftrightarrow{EF}$$ intersecting at $$O$$. Find the values of $$x, y$$ and $$z$$ it is being given that $$x : y : z = 2 : 3 : 5$$
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Two complementary angles are in the ratio $$4 : 5$$. Find the angles.



In the figure, find the values of $$x$$ and $$y$$ and then show that $$AB\parallel CD$$.
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Vertically opposite angle of $$\angle XVW$$ is _______.
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Write all pairs of vertically opposite angles.
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Vertically opposite angle of $$\angle XVZ$$ is __________.
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Find x:
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How many pair of vertically opposite angles are formed?
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Write the pair of vertically opposite angles.
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In the given figure , the arms of two angles are parallel. if      $$\angle ABC = {70^ \circ }$$  , then find 
(i)  $$\angle DGC$$
(ii) $$\angle DEF$$
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Fill in the blanks:
If two line intersect at a point and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are_______.



In the adjoining figure,$$p\parallel q$$. Find the unknown angles.
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In the given figure, if $$\angle A O C + \angle B O D = 266 ^ { \circ }$$ find all the four angles.
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In the given figure, find $$x$$.
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Corresponding angles are on the _________ side of the transversal.



The sum of two vertically opposite angles is $$166^\circ.$$ Find each of the angles.



A road crosses a railway line at an angle of $$30^o$$ as shown in Fig.
Find the values of $$a,\ b$$ and $$c$$.
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If two angles have a common vertex and their arms form opposite rays Fig., Then, how many types of angles are formed?
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Prove that the bisectors of a pair of vertically opposite angles are on the same straight line.



Name all the pairs of vertically opposite angles in the following figure.
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In the figure, if lines $$PQ$$ and $$RS$$ intersect at point $$T$$, such that $$\angle PRT={ 40 }^{\circ  }, \angle RPT={ 95 }^{\circ  }$$ and $$\angle TSQ={ 75 }^{\circ  }$$, find $$\angle SQT$$.
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Show that if a straight line is perpendicular to one of the two or more parallel lines, then it is also perpendicular to the remaining lines.



In the Fig.  lines PQ and RS intersect each other at point O. If $$\angle POR : \angle ROQ = 5 : 7$$, Find all the angles.
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$$P$$ is a point on the bisector of $$\angle ABC$$. The line through $$P$$ parallel to $$BA$$  meets $$BC$$ at $$Q$$. Prove that $$\Delta BPQ$$ is an isosceles triangle.



In the given figure, two lines $$AB$$ and $$CD$$ intersect at $$O$$. Ray $$OE$$ is perpendicular to the line $$AB$$. If $$a:b=3:7,$$ then find reflex $$\angle BOD$$.
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In the given figure if line segment $$PQ$$ and $$RS$$ intersect at point $$T$$, such that $$\angle PRT\, = \,40^\circ \,,\,\,\angle RPT\, = \,95^\circ \,\,and\,\,\angle TSQ\, = \,75^\circ \,,\,find\,\,\angle SQT$$.
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Two lines intersecting each other, prove that vertically opposite angles are equal.



In the given figure two lines $$AB$$ and $$CD$$ intersect at $$O,$$ $$OE$$  is any ray such that $$\angle BOE=80^{\circ}$$. If $$\angle BOD=30^{\circ}$$, then the find $$\angle EOC$$.
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Write  $$4$$ pairs of vertically opposite angles from the given figure
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Find the measure of $$b$$ in the following figures.
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In figure the value of $$x$$, hence find all three indicated angles.
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Find $$\dfrac{x+u+y+z}{50}$$
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find the value of x in each of the following figures.
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Observe the following figure and write each:
(i) Linear pair
(ii) Pair of vertically opposite angles
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Fill in the blanks:
_____pair of vertically opposite angle are formed by the intersection of $$2$$ lines



In the adjoining figure, identify the vertically opposite angles.
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In the given figure, lines $$AB$$ and $$CD$$ intersect at $$O$$.If $$\angle{AOC}+\angle{BOE}={70}^{\circ}$$ and $$\angle{BOD}={40}^{\circ}$$ find $$\angle{BOE}$$ and reflex of $$\angle{COE}$$
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In Fig., $$AB\parallel CD $$ and $$ \angle 1$$ and $$ \angle 2$$ are in the ratio 3:Determine all angles from 1 to 8.

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In Fig., PQ and RS intersect each other at point O. If $$ \angle POR : \angle ROQ = 5:7,$$ find all the angles.
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In figure, write another name for $$\angle 3$$.
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In figure, OE is the bisector of $$\angle BOD$$. If $$\angle 1=70^o$$, find the magnitudes of $$\angle 2, \angle 3$$ and $$\angle 4$$.
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Find the value of x in the following figure.
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In figure, lines $$l_1$$ and $$l_2$$ intersect at $$O$$, forming angles as shown in the figure. If $$x=45^o$$, find the values of $$y, z$$ and $$u$$.
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In the given figure, the corresponding arms of $$\angle ABC$$ and $$\angle DEF$$ are parallel. If $$\angle ABC=75^o$$, then find $$\angle DEF$$.
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In figure, three coplanar lines intersect at a point $$O$$, forming angles as shown in the figure. Find the values of $$x, y, z$$ and $$u$$.
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In figure, find the values of $$x, y$$ and $$z$$.
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If two straight lines intersect each other, then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.



Two lines $$AB$$ and $$CD$$ intersect at $$O$$. If $$\angle AOC={50}^{o}$$, find $$\angle AOD, \angle BOD$$ and $$\angle BOC$$
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In the figure, three coplanar lines $$AB,CD$$ and $$EF$$ intersect at a point $$O$$, forming angles as shown. Find the values of $$x,y,z$$ and $$t$$
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Two lines $$AB$$ and $$CD$$ intersect at a point $$O$$ such that $$\angle BOC+\angle AOD={280}^{o}$$, as shown in the figure. Find all four angles.
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If two straight lines intersect each other in such a way that one of the angles formed measures $${90}^{o}$$, show that each of the remaining angles measures $${90}^{o}$$.
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In the given figure, the two lines $$AB$$ and $$CD$$ intersect at a point $$O$$ such that $$\angle BOC={125}^{o}$$. Find the values of $$x,y$$ and $$z$$
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In the given figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$.
Name all the pairs of vertically opposite angles.
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In the given figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$.
Name all the pairs of adjacent angles.
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In the figure, three lines $$AB,CD$$ and $$EF$$ intersect at a point $$O$$ such that $$\angle AOE={35}^{o}$$ and $$\angle BOD={40}^{o}$$. Find the measure of $$\angle AOC,\angle BOF,\angle COF$$ and $$\angle DOE$$
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In the adjoining figure, it is being given that $$ AO \parallel CD, OB \parallel CE $$ and $$ \angle AOC=50^o $$. Find the measure of $$ \angle ECD $$.
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The legs of a stool make an angle of $$35^o$$ with the floor as shown in
Fig. Find the angle $$x$$ and $$y$$
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Three lines $$AB,\ CD$$ and $$EF$$ intersect each other at $$O$$. If $$\angle AOE=30^o$$ and $$\angle DOB=40^o$$ Fig. find $$\angle COF$$.
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In Fig., $$AB \parallel CD$$. Find the reflex $$\angle EFG$$.
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In Fig. , If $$RP =RQ$$, find the value of $$x$$

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Angles formed by two intersecting lines having no common arms are called ..



If two lines intersect and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are ..



Find the value of x in each of the following figures.
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In the given figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$.
Find the value of $$\angle a$$.
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The adjoining figure, shows two straight lines AB and CD intersecting at P. If $$\angle BPC = 4x - 5^\circ$$ and $$\angle APD = 3x + 15^\circ,$$ find the value of $$x$$.
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The adjoining figure, shows two straight lines AB and CD intersecting at P. If $$\angle BPC = 4x - 5^\circ$$ and $$\angle APD = 3x + 15^\circ,$$ find $$\angle BPD$$.
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Two straight lines AB and CD intersect each other at a point O and angle $$AOC = 50^\circ,$$ find: 
angle BOD.

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The adjoining figure, shows two straight lines AB and CD intersecting at P. If $$\angle BPC = 4x - 5^\circ$$ and $$\angle APD = 3x + 15^\circ,$$ then find $$\angle BPC$$.
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Identify the pair of angles given below by referring the given figure as adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
$$\angle 2$$ and $$\angle 4$$
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In the given figure, lines $$AB$$ and $$CD$$ intersect at point $$O$$.
Name all the reflex angles formed and write the measures of each.
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The adjoining figure, shows two straight lines AB and CD intersecting at P. If $$\angle BPC = 4x - 5^\circ$$ and $$\angle APD = 3x + 15^\circ,$$ find $$\angle APD$$.
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Identify the pair of angles given below by referring the given figure as adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
$$\angle 1$$ and $$\angle 10$$
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Identify the pair of angles given below by referring the given figure as adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
$$\angle 4$$ and $$\angle 5$$
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Identify the pair of angles given below by referring the given figure as adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
$$\angle 6$$ and $$\angle 12$$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 4 \quad and \quad \angle 6 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 7 \quad and \quad \angle 13 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 1 \quad and \quad \angle 8 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 5 \quad and \quad \angle 7 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 6 \quad and \quad \angle 8 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 10 \quad and \quad \angle 12 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 3 \quad and \quad \angle 6 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 1 \quad and \quad \angle 5 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 4 \quad and \quad \angle 6 $$
1828514_2f3c7f598a9941eba54411246af5fe9e.png



In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 2 \quad and \quad \angle 13 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 4 \quad and \quad \angle 5 $$
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In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 7 \quad and \quad \angle 9 $$
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 In the given figures, the directed lines are parallel to each other. Find the unknown angles.

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In the above figure, lines $$AB$$ and $$CD$$ intersect at $$O$$. If $$\angle AOC + \angle BOE = 70^{\circ} and \angle BOD = 40^{\circ} $$ , find $$\angle BOE $$ and reflex $$\angle COE$$
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Two lines are perpendicular to two parallel lines respectively. Show that these two lines are also parallel.
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Find the magnitude of $$\angle BOD$$



In figure, BA || ED and  BC || EF. Show that $$\angle ABC + \angle DEF = 180^o$$
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In the adjoining figure if lines $$ \mathrm{PQ} $$ and $$ \mathrm{RS} $$ intersect at point $$ T, $$ such that $$ \angle P R T=40^{\circ}, $$
$$ \angle \mathrm{RPT}=95^{\circ} $$ and $$ \angle \mathrm{TSQ}=75^{\circ}, $$ find $$ \angle \mathrm{SQT} $$
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Find the measure of $$x$$ in the given figure.
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In figure, HOPE is a parallelogram , Find the angle measure $$x , y$$ and $$z$$ . State the properties used to find them.

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Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.



In Fig. arms BA and BC of $$\angle ABC$$ are respectively parallel to arms ED and EF of $$\angle DEF$$. Prove that $$\angle ABC= \angle DEF$$.
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In Fig., line $$n$$ is a transversal to lines $$l$$ and $$m$$. Identify the following:
Angle alternate to $$\angle PQR$$ and angle corresponding to angles $$\angle RQF$$ and angle alternate to $$\ \angle PQE$$ in Fig.

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Class 7 Maths Extra Questions