In the figure, ∠HNS is a right-angled isosceles triangle. HS // KR , ∠QML = 50°, ∠NQP = 43° and ∠LPM = 61°. Find
- ∠HSN
- ∠MKR
- ∠PRQ
(a)
∠HSN
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠NQJ = 45° (Corresponding angles, SH//QJ)
∠MQK
= ∠NQP + ∠NQJ
= 43° + 45°
= 88°
∠MKR
= 180° - ∠QML - ∠MQK
= 180° - 50° - 88°
= 42° (Angles sum of triangle)
(c)
∠PQR
= 180° - ∠MQK
= 180° - 88°
= 92°(Angles in a straight line)
∠RPQ = ∠MPN = 61° (Vertically opposite angles)
∠PRQ
= 180° - ∠RPQ - ∠PQR
= 180° - 61° - 92°
= 27° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 27°