In the figure, HJK is parallel to NPQ and the line NK cuts ∠JNQ into half. Given that KN and JP are straight lines, ∠HJN = 49°, ∠NPM = 41° and ∠JMK = 115°, find
- ∠v
- ∠x
- ∠w
(a)
∠NMP = ∠JMK = 115° (Vertically opposite angles)
∠v
= 180° - 115° - 41°
= 24° (Angles sum of triangle)
(b)
∠x
= 180° - 24°
= 156° (Interior angles)
(c)
∠w
= 180° - 24° - 24° - 41°
= 90° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 156°; (c) 90°