The figure is not drawn to scale. NPRS is a square and MNS is an equilateral triangle. PQR is an isosceles triangle. MRQ is a straight line.
- Find ∠SMR.
- Find ∠PQR.
(a)
∠RSN = 90°
∠MSN = 60° (Equilateral triangle MSB)
∠MSR
= 90° + 60°
= 150°
∠SMR
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠MRP
= 90° - ∠MRS;
= 90° - 15°
= 75°
∠QRP
= 180° - ∠MRP
= 180° - 75°
= 105° (Angles on a straight line)
∠PQR
= (180° - ∠QRC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
