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Question
In a right angled triangle ABC, ∠B is right angle, ∠A is x + 1 and ∠C is 2x + 5. Find ∠A and ∠C
Solution
Given in ∆ABC ∠B = 90°
∠A = x + 1
∠B = 2x + 5
By angle sum property of triangle
Sum of three angles of ∆ABC = 180°
∠A + ∠B + ∠C = 180°
(x + 1) + 90° + (2x + 5) = 180°
x + 2x + 1° + 90° + 5° = 180°
3x + 96° = 180°
3x = 180° – 96° = 84°
x = `(84^circ)/3` = 28°
∠A = x + 1 = 28 + 1 = 29
∠C = 2x + 5
= 2(28) + 5
= 56 + 5
= 61
∴ ∠A = 29°
∠C = 61°
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