Question
In a ∆ABC, points P, Q and R are taken on AB, BC and
CA, respectively, such that BQ = PQ and QC = QR. If ∠ BAC = 75°, what is the measure of ∠ PQR (in degrees)?Solution
∠BAC = 75º ∠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°
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- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exactvalue.)
(1800.23 ÷ 29.98) + (816.32 ÷ 23.9) + 1634.11 = ?
1449.98 ÷ 50.48 × 10.12 = ? × 2.16
36.05 × 5.02 + 12.052 = ? + 9.09 × 4.04
(31.9)3 + (34.021)² - (16.11)3 - (42.98)² = ?
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