Question

Calculate the angles x, y and z if :

`x/3 = y/4 = z/5`

Answer 1

Let x = 3k, y = 4k and z = 5k

∠ADC = x + z = 8k and ∠ABC = x + y = 7k

(Exterior angle of a ∆ is equal to the sum of pair of interior opposite angles)

Also, ∠ABC + ∠ADC = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

`=>` 8k + 7k = 180°

`=>` 15k = 180°

∴ `k = 180^circ/15 = 12^circ`

∴ x = 3 × 12° = 36°

y = 4 × 12° = 48°

z = 5 × 12° = 60°