The figure is not drawn to scale. NP//RQ and QP//SN. Triangles NSP and PQR are isosceles triangles. Find
- ∠h
- ∠i.
(a)
∠PQR = ∠PNS = 78° (QP//SN, PN//QR)
∠NPS
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠QPR
= 180° - 78° - 78°
= 24° (Isosceles triangle)
∠h
= 180° - 78° - 51° - 24°
= 27° (Interior angles, PN//QR)
(b)
∠i
= 180° - 28° - 27°
= 125° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 125°