In the figure, ∠FLQ is a right-angled isosceles triangle. FQ // HP , ∠NKJ = 46°, ∠LNM = 41° and ∠JMK = 59°. Find
- ∠FQL
- ∠KHP
- ∠MPN
(a)
∠FQL
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠LNG = 45° (Corresponding angles, QF//NG)
∠KNH
= ∠LNM + ∠LNG
= 41° + 45°
= 86°
∠KHP
= 180° - ∠NKJ - ∠KNH
= 180° - 46° - 86°
= 48° (Angles sum of triangle)
(c)
∠MNP
= 180° - ∠KNH
= 180° - 86°
= 94°(Angles in a straight line)
∠PMN = ∠KML = 59° (Vertically opposite angles)
∠MPN
= 180° - ∠PMN - ∠MNP
= 180° - 59° - 94°
= 27° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 27°