The figure is not drawn to scale. Triangle RSQ is an isosceles triangle. Triangle NPQ is an equilateral triangle. ∠SQR is
25 of ∠PNQ and ∠PQS = ∠NQR.
- Find ∠PQS.
- Find ∠NRQ.
(a)
∠PQN = 60° (Equilateral triangle)
∠SQR
= ∠PQN x
25 = 60° x
25 = 24°
∠PQS = ∠NQR
∠PQS
= ∠PQN - ∠SQA) ÷ 2
= (60° - 24°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
(b)
∠NRQ
= 180° - ∠PNQ - ∠PQS
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 102°