Question

If the $\angle A,\angle B,$ and $\angle Cof△ABC$ satisfy the relation $\angle B–\angle A=\angle C–\angle B,$ then find the measure of $\angle B.$

• A. ${45}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${60}^o$

Given:
$\angle B–\angle A=\angle C–\angle B$
$2\angle B=\angle A+\angle C...\left(i\right)$
We know that,
The sum of angles of a triangle $={180}^o$
$\therefore \angle A+\angle B+\angle C={180}^o...\left(ii\right)$

From equations (i) and (ii), we get,
$2\angle B+\angle B={180}^o$
$\Rightarrow 3\angle B={180}^o$
$\Rightarrow \angle B=\frac{{180}^o}{3}$
$\Rightarrow \angle B={60}^o$