Question

Consider the figure:

If $\angle$B = ${50}^{\circ }$, $\angle$ACD = ${120}^{\circ }$, and x = 2y, then find the value of $\angle$A (in degrees).

___

Answer 1

Given, $\angle$ACD = ${120}^{\circ }$​
Hence, $\angle$ACB = ${60}^{\circ }$​ (linear pair)
Using angle sum property of triangle, in $\Delta ABC$, we have
$\angle A+\angle B+\angle C={180}^{\circ }$
Substiuting the given values, we have,
$\angle$A = ${70}^{\circ }$​