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.
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.
Updated On: Sep 10, 2024
- 117° and 54°
- 72° and 54°
- 117° and 63°
- 72° and 63°
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The Correct Option is C
Solution and Explanation
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°
∠P = 54°
We know that:
∠QIR = 90° + ∠\(\frac{P}{2}\)
= 90° + 27°
= 117°
∠QXR = 90° - ∠\(\frac{P}{2}\)
= 90° - 27°
= 63°
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