In aΔPQR, the bisectors of ∠Q and ∠R meet at point O, inside the triangle. If…
2024
In aΔPQR, the bisectors of ∠Q and ∠R meet at point O, inside the triangle. If ∠QOR = 107°, then the measure of ∠P is:
- A.
40°
- B.
23°
- C.
17°
- D.
34°
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Step-by-Step Calculation
Identify the Formula:
The angle formed by the intersection of two interior angle bisectors (in this case, angle QOR) is related to the third angle of the triangle (angle P) by the following formula:
Angle QOR = 90 degrees + (Angle P / 2)
Substitute the Given Values:
Given that Angle QOR = 107 degrees:
107 degrees = 90 degrees + (Angle P / 2)
Solve for Angle P:
Subtract 90 degrees from both sides:
107 degrees - 90 degrees = Angle P / 2
17 degrees = Angle P / 2
Multiply both sides by 2:
Angle P = 17 degrees * 2
Angle P = 34 degrees