In the figure, ∠EKP is a right-angled isosceles triangle. EP // GN , ∠MJH = 52°, ∠KML = 41° and ∠HLJ = 53°. Find
- ∠EPK
- ∠JGN
- ∠LNM
(a)
∠EPK
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠KMF = 45° (Corresponding angles, PE//MF)
∠JMG
= ∠KML + ∠KMF
= 41° + 45°
= 86°
∠JGN
= 180° - ∠MJH - ∠JMG
= 180° - 52° - 86°
= 42° (Angles sum of triangle)
(c)
∠LMN
= 180° - ∠JMG
= 180° - 86°
= 94°(Angles in a straight line)
∠NLM = ∠JLK = 53° (Vertically opposite angles)
∠LNM
= 180° - ∠NLM - ∠LMN
= 180° - 53° - 94°
= 33° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 33°
