In the figure, not drawn to scale, NPQR is a square, QRS is an equilateral triangle, QSTU is a rhombus, and PQ = SQ. Find
- ∠QUT
- ∠NSP
(a)
∠RQS = 60°
∠PQS
= 90° - 60°
= 30°
QS = QP
∠QSP
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠QUT
= ∠QSP
= 75° (Rhombus)
(b)
∠QPS = ∠QSP = 75°
∠NPS
= 90° - 75°
= 15°
∠NSP
= 180° - 15° - 15°
= 150° (Isosceles triangle NPS)
Answer(s): (a) 75°; (b) 150°