In the figure, FJMQ is a rectangle, MNQR is a rhombus and JKLM is a parallelogram. ∠MNQ = 80° and ∠LMN = 91°.
- Find ∠HMJ
- Find ∠MLK
(a)
∠QRM = ∠QNM = 80°
∠RMQ
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠HMJ
= 90° - 50°
= 40°
(b)
∠JML
= 360° - 91° - 90° - 50°
= 129° (Angles at a point)
∠KLM
= 180° - 129°
= 51° (Interior Angles, JM//KF)
Answer(s): (a) 40°; (b) 51°