Question

Question 110

In $\Delta XYZ$, the measure of $\angle X$ is ${30}^{\circ }$ greater than the measure of $\angle Y$ and $\angle Z$ is a right angle. Find measure of $\angle Y$

Answer 1

According to the question,
Measure of $\angle X=\angle Y+{30}^{\circ }$
Measure of $\angle Z={90}^{\circ }$
We know that, the sum of all three angles in a triangle is equal to ${180}^{\circ }$
i.e. $\angle X+\angle Y+\angle Z={180}^{\circ }$
$\Rightarrow (\angle Y+{30}^{\circ })+\angle Y+{90}^{\circ }={180}^{\circ }\Rightarrow 2\angle Y+{120}^{\circ }={180}^{\circ }\Rightarrow 2\angle Y={180}^{\circ }-{120}^{\circ }={60}^{\circ }\therefore \angle Y=\frac{{60}^{\circ }}{2}={30}^{\circ }$