In the figure, FJMQ is a rectangle, MNQR is a rhombus and JKLM is a parallelogram. ∠MNQ = 72° and ∠LMN = 97°.
- Find ∠HMJ
- Find ∠MLK
(a)
∠QRM = ∠QNM = 72°
∠RMQ
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠HMJ
= 90° - 54°
= 36°
(b)
∠JML
= 360° - 97° - 90° - 54°
= 119° (Angles at a point)
∠KLM
= 180° - 119°
= 61° (Interior Angles, JM//KF)
Answer(s): (a) 36°; (b) 61°