Question

In the given diagram O is the centre of the circle.If <QRS=105°,what is the value of <PQS? Find it.​

Answer 1

∠ PQS = 15°

Explanation:

PQRS is a cyclic quadrilateral

• the opposite angles of a cyclic quadrilateral sum to 180° , then

∠ QPS + ∠ QRS = 180°

∠ QPS + 105° = 180° ( subtract 105° from both sides )

∠ QPS = 75°

the sum of the 3 angles in Δ PQS = 180° , that is

∠ PQS + ∠ PSQ + ∠ QPS = 180°

∠ PQS + 90° + 75° = 180°

∠ PQS + 165° = 180° ( subtract 165° from both sides )

∠ PQS = 15°