Question

In a ∆PQR, internal angle bisectors of ∠Q and ∠R meet at I while external angle bisectors of ∠Q and ∠R meet at X. If ∠P = 54°, then find the measures of ∠QIR and ∠QXR, respectively.

• A. 117° and 54°
• B. 72° and 54°
• C. 117° and 63°
• D. 72° and 63°

Answer 1

Answer: (C)

117° and 63°

Answer 2

The correct option is (C): 117° and 63°

∠P = 54°
We know that:
∠QIR = 90° + ∠$\frac{P}{2}$
= 90° + 27°
= 117°
∠QXR = 90° - ∠$\frac{P}{2}$
= 90° - 27°
= 63°