CBSE Questions for Class 9 Maths Quadrilaterals Quiz 1 - MCQExams.com

$$\textbf{Step 1: Find x using angle sum property.}$$

              $$\text{We know, by angle sum property, the sum of angles of a quadrilateral is }360^o$$.

             $$\text{The given angles are }70^o,60^o,90^o,x$$.              $$\textbf{[Linear pairs are supplementary]}$$
             $$\text{Then, }70^o+60^o+90^o+x=360^o$$.

             $$\text{Therefore, the unknown angle is:}$$

             $$\Rightarrow$$ $$360^o - (70^o + 60^o + 90^o ) =x$$

             $$\Rightarrow$$ $$x=360^o - 220^o $$

                     $$ =140^{\circ}$$.

             $$\text{Therefore, the unknown angle is }x=140^o$$.

$$\textbf{Hence, option B is correct.}$$

Let the four angles be $$ \angle A , \angle B , \angle C$$ and $$\angle D$$ .

Then $$ \angle A =120^o, \angle B=73^o , \angle C = 80^o $$ .

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.

$$\implies$$ $$ \angle A + \angle B + \angle C + \angle D = 360^{o}  $$.

Then, $$  \angle D $$ will be given by:

$$\angle D = 360^o - \angle A - \angle B-\angle C $$ 

$$ \Rightarrow \angle D =  360 ^o-120^o -73^o -80^o $$ 

$$ \Rightarrow \angle D =  360 - 273^o$$

$$ \Rightarrow \angle D =  87^o$$.

The measure of fourth angle is $$ 87 ^{o}$$.

Therefore, option $$A$$ is correct.

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.

Here, the sum of angle will be $$= 110^o + 80^o + 90^o + 105^o = 385^o > 360^o$$.

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.

The given angles are $$50^o,130^o,120^o,x$$.
Then, $$50^o+130^o+120^o+x=360^o$$.

Therefore, the unknown angle is:

$$\Rightarrow$$ $$360^o - (50^o + 130^o + 120^o ) =x^{\circ}$$

$$\Rightarrow$$ $$x^o=360^o - 300^o  =60^{\circ}$$.

Therefore, the unknown angle is $$x^o=60^o$$.

Hence, option $$C$$ is correct.