The figure is not drawn to scale. QRTU is a square and PQU is an equilateral triangle. RST is an isosceles triangle. PTS is a straight line.
- Find ∠UPT.
- Find ∠RST.
(a)
∠TUQ = 90°
∠PUQ = 60° (Equilateral triangle PUB)
∠PUT
= 90° + 60°
= 150°
∠UPT
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠PTR
= 90° - ∠PTU;
= 90° - 15°
= 75°
∠STR
= 180° - ∠PTR
= 180° - 75°
= 105° (Angles on a straight line)
∠RST
= (180° - ∠STC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
