In the figure, not drawn to scale, PRST and NQTU are rhombuses. Given that ∠SRQ = 117° and ∠PNU = 126°, find
- ∠NUQ
- ∠QWP.
(a)
∠NUQ
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, NU = NR)
(b)
∠QPT
= 180° - 117°
= 63° (Interior angles, SR//TQ)
∠UQN = ∠NUQ = 27° (Isosceles Sriangle, NU = NR)
∠QWP
= 180° - 63° - 27°
= 90° (Angles sum of triangle, WQQ)
Answer(s): (a) 27°; (b) 90°