Question

Find all the three angles of the ΔABC

Answer 1

∠A + ∠B = ∠ACD ...(An exterior angle of a triangle is sum of its interior opposite angles)

x + 35 + 2x – 5 = 4x – 15

3x + 30 = 4x – 15

30 + 15 = 4x – 3x

45° = x

∠A = x + 35°

= 45° + 35°

= 80°

∠B = 2x – 5

= 2(45°) – 5°

= 90° – 5°

= 85°

∠ACD = 4x – 15

= 4(45°) – 15°

= 180° – 15°

= 165°

∠ACB = 180° – ∠ACD

= 180° – 165°

= 15°

∠A = 80°, ∠B = 85° and ∠C = 15°.