In the figure, ∠GMR is a right-angled isosceles triangle. GR // JQ , ∠PLK = 51°, ∠MPN = 42° and ∠KNL = 55°. Find
- ∠GRM
- ∠LJQ
- ∠NQP
(a)
∠GRM
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠MPH = 45° (Corresponding angles, RG//PH)
∠LPJ
= ∠MPN + ∠MPH
= 42° + 45°
= 87°
∠LJQ
= 180° - ∠PLK - ∠LPJ
= 180° - 51° - 87°
= 42° (Angles sum of triangle)
(c)
∠NPQ
= 180° - ∠LPJ
= 180° - 87°
= 93°(Angles in a straight line)
∠QNP = ∠LNM = 55° (Vertically opposite angles)
∠NQP
= 180° - ∠QNP - ∠NPQ
= 180° - 55° - 93°
= 32° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 32°