In the figure, ∠GMR is a right-angled isosceles triangle. GR // JQ , ∠PLK = 49°, ∠MPN = 40° and ∠KNL = 56°. Find
- ∠GRM
- ∠LJQ
- ∠NQP
(a)
∠GRM
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠MPH = 45° (Corresponding angles, RG//PH)
∠LPJ
= ∠MPN + ∠MPH
= 40° + 45°
= 85°
∠LJQ
= 180° - ∠PLK - ∠LPJ
= 180° - 49° - 85°
= 46° (Angles sum of triangle)
(c)
∠NPQ
= 180° - ∠LPJ
= 180° - 85°
= 95°(Angles in a straight line)
∠QNP = ∠LNM = 56° (Vertically opposite angles)
∠NQP
= 180° - ∠QNP - ∠NPQ
= 180° - 56° - 95°
= 29° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 29°
