Question

If the $\angle$A, $\angle$B and $\angle$C of $\Delta ABC$ satisfy the relation $\angle$B - $\angle$A = $\angle$C - $\angle$B, then find the measure of $\angle B.$

Answer 1

$\angle A+\angle B+\angle C={180}^{\circ }$

and $\angle$B-$\angle$A = $\angle$C-$\angle$B

$\Rightarrow$ $\angle$B+ $\angle$B = $\angle$A+ $\angle$C

$\Rightarrow$ $\angle$2B= $\angle$A+ $\angle$C

From (i),

$\angle$B+2$\angle$B = ${180}^{\circ }\Rightarrow 3B={180}^{\circ }$

$\therefore \angle B=\frac{{180}^{\circ }}{3}={60}^{\circ }$

Hence $\angle B={60}^{\circ }$