In the figure, FJMQ is a rectangle, MNQR is a rhombus and JKLM is a parallelogram. ∠MNQ = 76° and ∠LMN = 93°.
- Find ∠HMJ
- Find ∠MLK
(a)
∠QRM = ∠QNM = 76°
∠RMQ
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠HMJ
= 90° - 52°
= 38°
(b)
∠JML
= 360° - 93° - 90° - 52°
= 125° (Angles at a point)
∠KLM
= 180° - 125°
= 55° (Interior Angles, JM//KF)
Answer(s): (a) 38°; (b) 55°