In the figure, ∠HNS is a right-angled isosceles triangle. HS // KR , ∠QML = 46°, ∠NQP = 41° and ∠LPM = 53°. Find
- ∠HSN
- ∠MKR
- ∠PRQ
(a)
∠HSN
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠NQJ = 45° (Corresponding angles, SH//QJ)
∠MQK
= ∠NQP + ∠NQJ
= 41° + 45°
= 86°
∠MKR
= 180° - ∠QML - ∠MQK
= 180° - 46° - 86°
= 48° (Angles sum of triangle)
(c)
∠PQR
= 180° - ∠MQK
= 180° - 86°
= 94°(Angles in a straight line)
∠RPQ = ∠MPN = 53° (Vertically opposite angles)
∠PRQ
= 180° - ∠RPQ - ∠PQR
= 180° - 53° - 94°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 33°