In the figure, not drawn to scale, PRST and NQTU are rhombuses. Given that ∠SRQ = 119° and ∠PNU = 122°, find
- ∠NUQ
- ∠QWP.
(a)
∠NUQ
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, NU = NR)
(b)
∠QPT
= 180° - 119°
= 61° (Interior angles, SR//TQ)
∠UQN = ∠NUQ = 29° (Isosceles Sriangle, NU = NR)
∠QWP
= 180° - 61° - 29°
= 90° (Angles sum of triangle, WQQ)
Answer(s): (a) 29°; (b) 90°