Question

Find the measure of the angle $\angle x.$

• A. ${90}^o$
• B. ${100}^o$
• C. ${110}^o$
• D. Insufficient data

Answer 1

The correct option is C ${110}^o$

In $△XAZ$, $\angle XAZ$ is obtained by using the fact that the sum of all the interior angles of a triangle is ${180}^o.$
let $\angle XAZ=\angle a$
$\Rightarrow \angle a+{25}^o+{35}^o={180}^o$
$\Rightarrow \angle a={180}^o-{25}^o-{35}^o={120}^o$


We can see that $\angle XAZ$ is an exterior angle to $△YAZ$.

For $△YAZ$, we apply the fact that the sum of all the exterior angles of a triangle is ${360}^o.$

$\Rightarrow \angle x+{130}^o+{120}^o={360}^o$
$\Rightarrow \angle x={360}^o-{130}^o-{120}^o={110}^o$