Geometry Practice Test 2

PQRS is a cyclic quadrilateral
PQ is the diameter
∠QRP = 45°
∠PRQ = 90° (angle in a semicircle)
In ΔPQR,
∠QPR +∠PRQ+∠PQR = 180°
45° + 90° +∠PQR = 180°
∠PQR = 180° − (45° + 90°)
= 180° −135°
∠PQR = 45°
∠PQR +∠PSQ = 180° (sum of opposite angles is 180° in a cyclic quadrilateral)
45° +∠PSQ = 180°
∠PSQ = 180° − 45°
∠PSQ = 135°