Question

Two angles of a quadrilateral are ${89}^{\circ }$ and ${113}^{\circ }$. If the other two angles are equal, find the equal angles.

• A. ${69}^{\circ }$
• B. ${89}^{\circ }$
• C. ${158}^{\circ }$
• D. ${79}^{\circ }$

Answer 1

Answer: (D)

${79}^{\circ }$

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

Given two angles are ${89}^o$ & ${113}^o$ and the other two angles are equal.

Let the unknown angle be $x^o$.

So, $x+x+{89}^o+{113}^o={360}^o$

$\Rightarrow 2x+{202}^o={360}^o\Rightarrow 2x={360}^o-{202}^o={158}^o\Rightarrow x=\frac{{158}^o}{2}={79}^o.$

So unknown angles are ${79}^o$ each.

Therefore, option $D$ is correct.