Question

2. ◻PQRS is cyclic. ∠P = (5x – 13)o and ∠R = (4x + 4)o . Find the measures of ∠P and ∠R.

Answer 1

Given that, PQRS is a cyclic quadrilateral ; ∠P = (5x-13)° ; ∠R = (4x+4)°

So, Sum of opposite ∠s of a cyclic quadrilateral is 180°.

Hence, ∠P + ∠R = 180°

or, 5x-13+4x+4 = 180°

or, 9x-9 = 180°

or, 9x = 180°+9

or, 9x = 189°

or, x = 189°/9

or, x = 21°

So, ∠P = 5x-13 = 5*21-13 = 92°

and, ∠R = 4x+4 = 4*21+4 = 88°