Use the information given in the following figure to find : (i) x (ii) ∠B and ∠C
Answer
∵ ∠A = 90˚ (Given)
∠B = (2x + 4˚)
∠C = (3x - 5˚)
∠D = (8x - 15˚)
∠A + ∠B + ∠C + ∠D = 360˚
90˚ + (2x + 4) + (3x - 5) + (8x - 15) = 360
⇒ 90 + 2x + 4 + 3x - 5 + 8x - 15 = 360
⇒ 74˚ + 13x = 360˚
⇒ 13x = 360˚ - 74˚
⇒ 13x = 286˚
⇒ x = 22˚
∵ ∠B = 2x + 4 = 2×22˚ + 4 = 48˚
∠C = 3x - 5 = 3 × 22˚ - 5 = 61˚
Hence (i)22˚ (ii) ∠B = 48˚, ∠C = 61˚