Question

In the given figure RISK and CLUE are parallelograms and $\angle R={70}^{\circ }$ and $\angle L$ is half of $\angle ESI$ Find the measure of x

• A. ${75}^{\circ }$
• B. ${55}^{\circ }$
• C. ${65}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${75}^{\circ }$

RISK and CLUE are parallelograms.
$\angle R={70}^{\circ }$
So, $\angle R=\angle ESI={70}^{\circ }$
$\angle L=1/2\angle ESI$
So, $\angle L=\angle CEU=1/2\angle ESI=70$
So, in triangle EXS
$\angle ESI+\angle CEU+\angle X=180$
$70+1/2\ast 70+\angle X=180$
$\angle X=180-105=75$
Answer (A) $75$