Question

Consider the figure:

If $BC=AC,x=2y,$ and angle $\angle ACB={60}^{\circ },$ then the value of $\angle B+y$ is ___ (in degrees).

Answer 1

Given, $\angle C={60}^{\circ }$ and $BC=AC,$
$\because AC=BC,△ABC$ is isosceles $\Rightarrow \angle A=\angle B={60}^{\circ }$

From exterior angle property, $x+y=\angle A+\angle B=60+60={120}^{\circ }$

$\Rightarrow x+y={120}^{\circ }$

Since, $x=2y$​
$\Rightarrow x+y=2y+y=3y={120}^{\circ }$​

$\Rightarrow y=\frac{120}{3}={40}^{\circ }$​

Hence, $\angle B+y=60+40={100}^{\circ }$​