In the figure, ∠HNS is a right-angled isosceles triangle. HS // KR , ∠QML = 49°, ∠NQP = 39° and ∠LPM = 58°. Find
- ∠HSN
- ∠MKR
- ∠PRQ
(a)
∠HSN
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠NQJ = 45° (Corresponding angles, SH//QJ)
∠MQK
= ∠NQP + ∠NQJ
= 39° + 45°
= 84°
∠MKR
= 180° - ∠QML - ∠MQK
= 180° - 49° - 84°
= 47° (Angles sum of triangle)
(c)
∠PQR
= 180° - ∠MQK
= 180° - 84°
= 96°(Angles in a straight line)
∠RPQ = ∠MPN = 58° (Vertically opposite angles)
∠PRQ
= 180° - ∠RPQ - ∠PQR
= 180° - 58° - 96°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 47°; (c) 26°
