Question

Two angles of a quadrilateral are equal and the other two angles are ${70}^o$ and ${80}^o$. Then the equal angles are:

• A. ${210}^{\circ }$
• B. ${105}^{\circ }$
• C. ${15}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is B ${105}^{\circ }$

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

Given two angles are equal.

Then $\angle A=\angle B=x$.

Also, $\angle C={70}^o$ and $\angle D={80}^o$.

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

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

$x+x+{70}^o+{80}^o={360}^o$

$2x+{150}^o={360}^o$

$\Rightarrow 2x={360}^o-{150}^o$

$\Rightarrow 2x={210}^o$

$\Rightarrow x={105}^o$.

Hence, the equal angles are $={105}^o$ each

Therefore, option $B$ is correct.