Q6 of 54 Page 77

Sum of two angles of a triangle is 90° and their difference is 50°. Find all the angles of the triangle.

In ΔABC


∠A + ∠C = 90° ……(1)


∠A + ∠B + ∠C = 180° (Angle Sum Property)


90° + ∠B = 180˚ ( from 1)


∠B = 90˚


Difference of ∠A and ∠C is 50°


∠A – ∠C = 50° ……(2)


Eliminate (1) and (2)


∠A + ∠C = 90°


∠A – ∠C = 50°


2×∠A = 140°


∠A = 70°


Put ∠A = 70° in (1)


∠A + ∠C = 90°


70° + ∠C = 90°


∠C = 20°


∴ ∠A = 70°


∠B = 90°


∠C = 20°


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