In the figure, FJMQ is a rectangle, MNQR is a rhombus and JKLM is a parallelogram. ∠MNQ = 74° and ∠LMN = 95°.
- Find ∠HMJ
- Find ∠MLK
(a)
∠QRM = ∠QNM = 74°
∠RMQ
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠HMJ
= 90° - 53°
= 37°
(b)
∠JML
= 360° - 95° - 90° - 53°
= 122° (Angles at a point)
∠KLM
= 180° - 122°
= 58° (Interior Angles, JM//KF)
Answer(s): (a) 37°; (b) 58°