Question

Quadrilateral $ABCD$ and $ECBA$ are inscribed in a circle. If $\angle B={125}^{\circ },$ find the measure of $\angle E.$

• A. ${55}^{\circ }$
• B. ${125}^{\circ }$
• C. ${130}^{\circ }$
• D. ${62.5}^{\circ }$

Answer 1

The correct option is A ${55}^{\circ }$

In a cyclic quadrilateral, we know, opposite angles are supplementary.

Since $AECB$ is a cyclic quadrilateral,

$\angle E+\angle B={180}^{\circ }$

$\angle E={180}^{\circ }-\angle B$

$={180}^{\circ }–{125}^{\circ }$

$={55}^{\circ }$

Hence, option $A$ is correct.