In the figure, ∠EKP is a right-angled isosceles triangle. EP // GN , ∠MJH = 49°, ∠KML = 37° and ∠HLJ = 59°. Find
- ∠EPK
- ∠JGN
- ∠LNM
(a)
∠EPK
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠KMF = 45° (Corresponding angles, PE//MF)
∠JMG
= ∠KML + ∠KMF
= 37° + 45°
= 82°
∠JGN
= 180° - ∠MJH - ∠JMG
= 180° - 49° - 82°
= 49° (Angles sum of triangle)
(c)
∠LMN
= 180° - ∠JMG
= 180° - 82°
= 98°(Angles in a straight line)
∠NLM = ∠JLK = 59° (Vertically opposite angles)
∠LNM
= 180° - ∠NLM - ∠LMN
= 180° - 59° - 98°
= 23° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 49°; (c) 23°
