The figure is not drawn to scale. LMQ is an equilateral triangle and PMN is an isosceles triangle. NML and MPR are straight lines and NL//RQ. ∠QMR = 90° and ∠PQM = 53°.
- Find ∠NMR.
- Find ∠MPN.
- Find ∠QPR.
(a)
∠QML = 60° (Equilateral triangle LMY)
∠QMR = 90°
∠PQM = 53°
∠NMR
= 180° - ∠QMR - ∠QML
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠MPN
= (180° - ∠NMR ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠QPM
= 180° - ∠QMR - ∠PQM
= 180° - 90° - 53°
= 37°
∠QPR
= 180° - ∠QPM
= 180° - 37°
= 143° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 143°
