In the figure, not drawn to scale, PRST and NQTU are rhombuses. Given that ∠SRQ = 113° and ∠PNU = 124°, find
- ∠NUQ
- ∠QWP.
(a)
∠NUQ
= (180° - 124°) ÷ 2
= 56 ÷ 2
= 28° (Isosceles triangle, NU = NR)
(b)
∠QPT
= 180° - 113°
= 67° (Interior angles, SR//TQ)
∠UQN = ∠NUQ = 28° (Isosceles Sriangle, NU = NR)
∠QWP
= 180° - 67° - 28°
= 85° (Angles sum of triangle, WQQ)
Answer(s): (a) 28°; (b) 85°