Question

In a right angled triangle ABC, ∠B is right angle, ∠A is x + 1 and ∠C is 2x + 5. Find ∠A and ∠C.

Answer 1

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°