Q11 of 34 Page 170

The sum of two angles of a triangle is 80° and their difference is 20°. Find the angles of the triangle.

In a triangle ABC, it is given that


∠A – ∠B = 20° … (1)


and ∠A + ∠B = 80° .. (2)


Add (1) and (2),


⇒ 2∠A = 100°


⇒ ∠A = 50°


So, ∠B = 80° - ∠A = 80° - 50° = 30°


We know that the sum of the angles of a triangle is 180°.


⇒ ∠A + ∠B + ∠C = 180°


⇒ 50° + 30° + ∠C = 180°


⇒ ∠C = 180° - 80°


⇒ ∠C = 100°


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