NPQR is a square. MLQ and PLR are straight lines. PN = PM and ∠LPM = 15°. Find
- ∠PNM
- ∠RQM
.
(a)
∠NPR = 45° (Right angle)
∠NPM
= ∠NPR - ∠LPM
= 45° - 15°
= 30°
∠PNM
= (180° - ∠NPM) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
PN = PM = PQ
MPQ is an isosceles triangle.
∠PMQ = ∠PQM (Isosceles triangle)
∠PQM
= (180° - ∠RPQ - ∠LPM) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠RQM
= ∠PQR - ∠PQM
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
