Quadrilateral PQRS is inscribed in a circle. If ∠P = (2x + 10)° and ∠R = (3x - 20)°, find the value of x Class 9

Quadrilateral PQRS is inscribed in a circle. If ∠P = (2x + 10)° and ∠R = (3x - 20)°, find the value of x Class 9

Question 1.

Quadrilateral PQRS is inscribed in a circle. If ∠P = (2x + 10)° and ∠R = (3x - 20)°, find the value of x and the measures of : ∠P and ∠R. Class 9

Solution:

PQRS is a cyclic quadrilateral.

Since the sum of two opposite angles of a cyclic quadrilateral is 180°

∴ ∠P + ∠R = 180°

∴ (2x + 10) + (3x - 20) = 180

∴ 5x - 10 = 180

∴ 5x = 190

∴ x = $\frac{190}{5}$ = 38

∠P = 2 (38) + 10 = 76 + 10 = 86°

∠R = 3 (38) - 20 = 114 - 20 = 94°