The figure is not drawn to scale. NP//RQ and QP//SN. Triangles NSP and PQR are isosceles triangles. Find
- ∠d
- ∠e.
(a)
∠PQR = ∠PNS = 74° (QP//SN, PN//QR)
∠NPS
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠QPR
= 180° - 74° - 74°
= 32° (Isosceles triangle)
∠d
= 180° - 74° - 53° - 32°
= 21° (Interior angles, PN//QR)
(b)
∠e
= 180° - 30° - 21°
= 129° (Angles sum of triangle)
Answer(s): (a) 21°; (b) 129°
