The figure is not drawn to scale. MNQR is a square and LMR is an equilateral triangle. NPQ is an isosceles triangle. LQP is a straight line.
- Find ∠RLQ.
- Find ∠NPQ.
(a)
∠QRM = 90°
∠LRM = 60° (Equilateral triangle LRB)
∠LRQ
= 90° + 60°
= 150°
∠RLQ
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠LQN
= 90° - ∠LQR;
= 90° - 15°
= 75°
∠PQN
= 180° - ∠LQN
= 180° - 75°
= 105° (Angles on a straight line)
∠NPQ
= (180° - ∠PQC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
