1.

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°

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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