CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 3 - MCQExams.com

$$\angle AOB = \angle DOC = 105^{\circ}$$

We know that an open curve has two end points.

The point $$R$$ is one the curve.
Hence, option C is correct.

$$P$$ is point is interior of curve.

We know that an open curve has two end points and a closed curve has no end points because its starting and ending points are same.

We know that an open curve has two end points and a curve which begins and ends at the same point is called a closed curve.

The point $$Q$$ is on the curve.

We know that an open curve has two end points and a curve which begins and ends at the same point is called a closed curve.

We know that an open curve has two endpoints and a curve that begins and ends at the same point is called a closed curve.

A curve which begins and ends at the same point is called a closed curve.

The points $$S$$ and $$T$$ are in the exterior of the curve.

The point $$P$$ is in the interior of curve.

The point which is on the curve is $$B$$.
Hence, option B is correct.

if each pair of opposite sides of a quadrilateral is equal and parallel then it is a parallelogram (property of parallelogram)

Two opposite angles of a parallelogram are $$(3x-2)^o$$ and $$(50-x)^o$$

Let $$\angle A, \angle B, \angle C,\angle D$$ be the four angles of the parallelogram ABCD, Such that $$\angle B$$ and $$\angle D$$ are opposite angles and also $$\angle A$$ and $$\angle C $$ are the opposite angles.

Let $$\angle A = 70^o$$, then $$\angle C=70^o$$      {opposite angles are equal} 

Angle adjacent to $$\angle A = \angle D=180^o-70^o$$

                                                  $$=110^o$$

Also, $$\angle D = \angle B = 110^o$$                          {Opposite angles}

$$So\>angles\>are\>70^\circ,110^\circ,70^\circ,110^\circ\>(complete\>set)$$

As the diagonal of quadrilateral bisects each other; 5b-4=3b+6
2b=10
$$b=5$$
So by the same rule;3b-4=2a
15-4=2a
11=2a
$$a=\dfrac{11}{2}$$

The above statement is not true for every parallelogram.

We know that, diagonals of a parallelogram bisect each other.

False, as it doesn't have all it's angles equal.

A kite is a convex quadrilateral.

Pentagon has $$ 5 $$ sides but this figures has $$ 6 $$ sides.

$$ After\quad analysing\quad the\quad given\quad table\quad it\quad is\quad observed\quad that\quad when\\ (i)\quad numbre\quad of\quad sides\quad of\quad the\quad polygon=3\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \longrightarrow sum\quad of\quad the\quad internal\quad angles={ 180 }^{ o }=\left( 3-2 \right) \times { 180 }^{ o }\\ (ii)\quad numbre\quad of\quad sides\quad of\quad the\quad polygon=4\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \longrightarrow sum\quad of\quad the\quad internal\quad angles={ 360 }^{ o }=\left( 4-2 \right) \times { 180 }^{ o }\\ (iii)\quad numbre\quad of\quad sides\quad of\quad the\quad polygon=5\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \longrightarrow sum\quad of\quad the\quad internal\quad angles={ 540 }^{ o }=\left( 5-2 \right) \times { 180 }^{ o }\\ (iv)\quad numbre\quad of\quad sides\quad of\quad the\quad polygon=6\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \longrightarrow sum\quad of\quad the\quad internal\quad angles={ 720 }^{ o }=\left( 6-2 \right) \times { 180 }^{ o }\\ \therefore \quad By\quad induction,\quad it\quad can\quad be\quad concluded\quad that\\ When\quad the\quad numbre\quad of\quad sides\quad of\quad the\quad polygon=n\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \longrightarrow sum\quad of\quad the\quad internal\quad angles=\left( n-2 \right) \times { 180 }^{ o }\\ \therefore \quad For\quad a\quad 7\quad sided\quad polygon\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \rightarrow sum\quad of\quad the\quad internal\quad angles=\left( 7-2 \right) \times { 180 }^{ o }={ 900 }^{ o }\\ \\ \\ \\ \\ \\ \\  $$

$$ A\quad simple\quad closed\quad curve\quad encloses\quad a\quad single\quad area \quad and \quad do \quad not\quad have  \quad intersecting \quad lines.\\ Here\quad in\quad each\quad of\quad the\quad figures\quad 1,\quad 2,\quad 5,\quad 6,\quad 7\quad a\quad single\quad area\\ is\quad enclosed.\\ But\quad in\quad each\quad of\quad the\quad figures\quad 3,\quad 4,\quad 8\quad more\quad than\quad one\quad area\\ are\quad enclosed.\\ So\quad each\quad of\quad the\quad figures\quad 1,\quad 2,\quad 5,\quad 6,\quad 7\quad is\quad a\quad simple\quad closed \quad curve.\\ $$

Here, let the number of sides of the polygon be $$n.$$

$$ ABCD$$ and $$ AEFG$$ are two parallelograms sharing two sides $$AD$$ (or $$AG$$) and $$AE$$ (or $$AE$$) and the included angle. 

Let $$ABCD$$ be a quadrilateral.

In given figure,