The sides AB and AC of ΔABC are produced to P and Q respectively. The bisectors of ∠CBP and ∠BCQ meet at R. If the measure of ∠A = 44°, the find the measure of ∠BRC/2.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 34.
As we know,
⇒ ∠ABC + ∠CBP = 180°
⇒ ∠CBP = 180° – ∠ABC
⇒ ∠CBP/2 = 90° – ∠ABC/2
Similarly,
⇒ ∠BCR/2 = 90° – ∠ACB/2
In ΔBRC
⇒ ∠CBP/2 + ∠BCR/2 + ∠BRC = 180°
⇒ 90° – ∠ABC/2 + 90° – ∠ACB/2 + ∠BRC = 180°
⇒ 180° – ∠ABC/2 – ∠ACB/2 + ∠BRC = 180°
⇒ ∠BRC = 180° – 180° + (∠ABC + ∠ACB)/2
⇒ ∠BRC = (180° – ∠BAC)/2
⇒ ∠BRC = 90° – ∠BAC/2
⇒ ∠BRC = 90° – 44°/2
⇒ ∠BRC = 90° – 22 = 68
⇒ ∠BRC/2 = 68°/2 = 34°