The figure is not drawn to scale. PQST is a square and NPT is an equilateral triangle. QRS is an isosceles triangle. NSR is a straight line.
- Find ∠TNS.
- Find ∠QRS.
(a)
∠STP = 90°
∠NTP = 60° (Equilateral triangle NTB)
∠NTS
= 90° + 60°
= 150°
∠TNS
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠NSQ
= 90° - ∠NST;
= 90° - 15°
= 75°
∠RSQ
= 180° - ∠NSQ
= 180° - 75°
= 105° (Angles on a straight line)
∠QRS
= (180° - ∠RSC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
