In the figure, not drawn to scale, MNPQ is a square, PQR is an equilateral triangle, PRST is a rhombus, and NP = RP. Find
- ∠PTS
- ∠MRN
(a)
∠QPR = 60°
∠NPR
= 90° - 60°
= 30°
PR = PN
∠PRN
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠PTS
= ∠PRN
= 75° (Rhombus)
(b)
∠PNR = ∠PRN = 75°
∠MNR
= 90° - 75°
= 15°
∠MRN
= 180° - 15° - 15°
= 150° (Isosceles triangle MNR)
Answer(s): (a) 75°; (b) 150°