The figure is not drawn to scale. MN//QP and PN//RM. Triangles MRN and NPQ are isosceles triangles. Find
- ∠b
- ∠c.
(a)
∠NPQ = ∠NMR = 72° (PN//RM, NM//PQ)
∠MNR
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠PNQ
= 180° - 72° - 72°
= 36° (Isosceles triangle)
∠b
= 180° - 72° - 54° - 36°
= 18° (Interior angles, NM//PQ)
(b)
∠c
= 180° - 26° - 18°
= 136° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 136°
