Q111 of 158 Page 159

In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

Given: ∠A is 40° less than ∠B


∠A is 50° less than ∠C


Formula Used/Theory:-


→ Angle sum property


Sum of all angles of triangle is 180°


Let ∠A be ‘x’


Then;


⇒ ∠A = ∠B - 40°


x = ∠B - 40°


∠B = x + 40°


⇒ ∠A = ∠C - 50°


x = ∠C - 50°


∠C = x + 50°


By angle sum property


∠A + ∠B + ∠C = 180°


x + (x + 40°) + (x + 50°) = 180°


3x + 90° = 180°


3x = 180° - 90° = 90°


x = = 30°


∠A = x


∴ ∠A = 30°


Result:- Measure of ∠A comes out to be 30°


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