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In ΔABC, ∠A - ∠B = 33°, ∠B - ∠C = 18° What is the sum of the smallest and the largest angles of the triangle?1.92° 2. 143° 3. 125° 4. 108° |
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Answer» Correct Answer - Option 3 : 125° GIVEN: ∠A - ∠B = 33°, ∠B - ∠C = 18° CALCULATION: ∠A - ∠B = 33°, ∠B - ∠C = 18° ⇒ ∠A = 33° + ∠B and ∠C = ∠B - 18° ⇒ ∠A + ∠B + ∠C = 180° ⇒ ∠B + 33° + ∠B + ∠B - 18° = 180° ⇒ 3∠B = 180° - 15° ⇒ 3∠B = 165° ⇒ ∠B = 55° ⇒ ∠A = 33° + 55° = 88° ⇒ ∠C = 55° - 18° = 37° ⇒ The largest angle A = 88° and the smallest angle C = 37° ⇒ Sum of the smallest and the largest angle = (88° + 37° ) = 125° ∴ Sum of the smallest and the largest angle is 125° |
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