The figure is not drawn to scale. MNR is an equilateral triangle and QNP is an isosceles triangle. PNM and NQS are straight lines and PM//SR. ∠RNS = 90° and ∠QRN = 54°.
- Find ∠PNS.
- Find ∠NQP.
- Find ∠RQS.
(a)
∠RNM = 60° (Equilateral triangle MNY)
∠RNS = 90°
∠QRN = 54°
∠PNS
= 180° - ∠RNS - ∠RNM
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠NQP
= (180° - ∠PNS ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠RQN
= 180° - ∠RNS - ∠QRN
= 180° - 90° - 54°
= 36°
∠RQS
= 180° - ∠RQN
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 144°
