Point O is the incenter of triangle ABC. What is m QOB? 30°, 60°, 75°, 90°

Solution:

Given, O is the incenter of triangle ABC.

We have to find the measure of QOB.

Incenter of a triangle is the meeting point of the three angle bisectors of a triangle.

So, m ∠QBO = m ∠OBR

From the figure,

m ∠OBR = 15°

So, m ∠QBO = 15°

We know that the sum of internal angles in a triangle must be equal to 180

So, in right triangle OQB

m ∠QBO + m ∠QOB + 90° = 180°

Now, 15° + m ∠QOB + 90° = 180°

On rearranging,

15° + 90° + m ∠QOB = 180°

105° + m ∠QOB = 180°

m ∠QOB = 180° - 105°

m ∠QOB = 75°

Therefore, m QOB = 75°.

Point O is the incenter of triangle ABC. What is m QOB? 30°, 60°, 75°, 90°

Summary:

Point O is the incenter of triangle ABC, then m QOB is 75°.