Question

Consider the figure:

If $\angle A={50}^{\circ }$​, $\angle ACD={120}^{\circ }$​, and $x=2y,$ then $\angle B=$ ___ ${}^{\circ }$.

Answer 1

Given, $\angle ACD={120}^{\circ }$​
Hence, $\angle ACB=180-120={60}^{\circ }$​ [linear pair]

Using angle sum property of triangle, in $△ABC$, we have
$\angle A+\angle B+\angle C={180}^{\circ }$
Substiuting the given values, we have,
$\angle B=180-\angle A-\angle C$

$=180-50-60={70}^{\circ }$​