Question

If the sum of measure of angles $\angle B,\angle A$ and $\angle E$ is ${90}^o,$ find the measure of each individual angle, i.e., $\angle B,\angle A$ and $\angle E.$

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$

Answer 1

The correct option is A ${30}^o$

For the given figure,
Arc CD subtends angle $\angle B$ at B, $\angle A$ at A and $\angle E$ at E.

We know that the measure of all angles subtended by an arc on the same segment of the circle are equal.

$\therefore \angle B=\angle A=\angle E$
Given, $\angle B+\angle A+\angle E={90}^o$
$\Rightarrow 3\times \angle B={90}^o$
$\Rightarrow \angle B=\frac{{90}^o}{3}={30}^o$

$\therefore$ Each individual angles are ${30}^o$ in measure.