In the figure, FJMQ is a rectangle, MNQR is a rhombus and JKLM is a parallelogram. ∠MNQ = 78° and ∠LMN = 96°.
- Find ∠HMJ
- Find ∠MLK
(a)
∠QRM = ∠QNM = 78°
∠RMQ
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠HMJ
= 90° - 51°
= 39°
(b)
∠JML
= 360° - 96° - 90° - 51°
= 123° (Angles at a point)
∠KLM
= 180° - 123°
= 57° (Interior Angles, JM//KF)
Answer(s): (a) 39°; (b) 57°