In the figure, KNRU is a rectangle, RSUV is a rhombus and NPQR is a parallelogram. ∠RSU = 74° and ∠QRS = 91°.
- Find ∠MRN
- Find ∠RQP
(a)
∠UVR = ∠USR = 74°
∠VRU
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠MRN
= 90° - 53°
= 37°
(b)
∠NRQ
= 360° - 91° - 90° - 53°
= 126° (Angles at a point)
∠PQR
= 180° - 126°
= 54° (Interior Angles, NR//PF)
Answer(s): (a) 37°; (b) 54°