In the figure, ∠FLQ is a right-angled isosceles triangle. FQ // HP , ∠NKJ = 47°, ∠LNM = 43° and ∠JMK = 55°. Find
- ∠FQL
- ∠KHP
- ∠MPN
(a)
∠FQL
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠LNG = 45° (Corresponding angles, QF//NG)
∠KNH
= ∠LNM + ∠LNG
= 43° + 45°
= 88°
∠KHP
= 180° - ∠NKJ - ∠KNH
= 180° - 47° - 88°
= 45° (Angles sum of triangle)
(c)
∠MNP
= 180° - ∠KNH
= 180° - 88°
= 92°(Angles in a straight line)
∠PMN = ∠KML = 55° (Vertically opposite angles)
∠MPN
= 180° - ∠PMN - ∠MNP
= 180° - 55° - 92°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 45°; (c) 33°
