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प्रश्न
Calculate the angles x, y and z if :
`x/3 = y/4 = z/5`
उत्तर
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°
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