The figure is not drawn to scale. LMPQ is a square and KLQ is an equilateral triangle. MNP is an isosceles triangle. KPN is a straight line.
- Find ∠QKP.
- Find ∠MNP.
(a)
∠PQL = 90°
∠KQL = 60° (Equilateral triangle KQB)
∠KQP
= 90° + 60°
= 150°
∠QKP
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠KPM
= 90° - ∠KPQ;
= 90° - 15°
= 75°
∠NPM
= 180° - ∠KPM
= 180° - 75°
= 105° (Angles on a straight line)
∠MNP
= (180° - ∠NPC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
