If a ∆ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠BAC = 75º, what is the measure of ∠ PQR (in degrees)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 30
∠BAC = 75°
∠ABC + ∠ACB + ∠BAC = 180°
∠ABC + ∠ACB + 75° = 180°
∠ABC + ∠ACB = 180° - 75° = 105°
Let, ∠ABC= ∠PBQ = 70° and ∠ACB = ∠RCQ = 35°
So, ∠PQR = 180° - (∠PQB + ∠RQC)
= 180°- [(180° - 2∠PBQ) + (180° - 2∠RQC) [ BQ = PQ; QC = QR]
= 180°- [(180° - 2 × 70°) + (180° - 2 × 35°)]
= 180°- (40° + 110°)
= 180° - 150°
= 30°