Exams › SSC CGL (Prelims) › General

In triangle $XYZ$, if the angle bisectors of $\angle Y$ and $\angle Z$ intersect at point $O$, and $\angle X = 70^\circ$, what is the measure of $\angle YOZ$?

1. 115°
2. 120°
3. 130°
4. 125°

Correct answer: 125°

Solution

Since $O$ is the incenter, the angle between the bisectors of $\angle Y$ and $\angle Z$ is $\angle YOZ = 90^\circ + \frac{\angle X}{2}$. With $\angle X = 70^\circ$, we get $90^\circ + 35^\circ = 125^\circ$.

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