The figure is not drawn to scale. NP//RQ and QP//SN. Triangles NSP and PQR are isosceles triangles. Find
- ∠p
- ∠q.
(a)
∠PQR = ∠PNS = 70° (QP//SN, PN//QR)
∠NPS
= (180° - 70°) ÷ 2
= 110° ÷ 2
= 55° (Isosceles triangle)
∠QPR
= 180° - 70° - 70°
= 40° (Isosceles triangle)
∠p
= 180° - 70° - 55° - 40°
= 15° (Interior angles, PN//QR)
(b)
∠q
= 180° - 26° - 15°
= 139° (Angles sum of triangle)
Answer(s): (a) 15°; (b) 139°