In the figure, not drawn to scale, PQRS is a square, RST is an equilateral triangle, RTUV is a rhombus, and QR = TR. Find
- ∠RVU
- ∠PTQ
(a)
∠SRT = 60°
∠QRT
= 90° - 60°
= 30°
RT = RQ
∠RTQ
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠RVU
= ∠RTQ
= 75° (Rhombus)
(b)
∠RQT = ∠RTQ = 75°
∠PQT
= 90° - 75°
= 15°
∠PTQ
= 180° - 15° - 15°
= 150° (Isosceles triangle PQT)
Answer(s): (a) 75°; (b) 150°