In triangle PQR, the bisectors of angles Q and R meet at point O inside the triangle. If the measure of angle QOR is 107°, what is the measure of angle P?

Question

Accepted Answer

Let the angles of triangle PQR be ∠P, ∠Q, and ∠R.

Given that the bisectors of ∠Q and ∠R meet at point O inside the triangle.

We know that O is the incenter of the triangle formed by the bisectors of angles Q and R.

The angle formed at O between the bisectors of ∠Q and ∠R is given by:

∠QOR = 90° + (∠P / 2)

Given ∠QOR = 107°

So,
107° = 90° + (∠P / 2)

Subtract 90° from both sides:
107° - 90° = ∠P / 2
17° = ∠P / 2

Multiply both sides by 2:
∠P = 34°

Therefore, the measure of angle P is 34°.

Answer

Answer

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