PSLE In the figure, GHMN is a parallelogram and JKLM is a rhombus. NML is a straight line. ∠HGN = 56°, ∠MHJ = 27° and ∠KJL = 33°.
- Find ∠HMJ.
- Find ∠HJK.
(a)
∠HMN
= ∠HGN
= 56° (Parallelogram)
∠KLJ
= ∠KJL
= 33° (Isosceles triangle)
∠JKL
= 180° - 33° - 33°
= 104° (Angles sum of triangle)
∠JML
= ∠JKL
= 104° (Rhombus)
∠HMJ
= 180° - 56° - 104°
= 20° (Angles on a straight line)
(b)
∠HJM
= 180° - 27° - 20°
= 133° (Angles sum of triangle)
∠LJM
= ∠KJL
= 33° (Rhombus)
∠HJK
= 360° - 133° - 33° - 33°
= 161° (Angles at a point)
Answer(s): (a) 20°; (b) 161°