In the figure, KNRU is a rectangle, RSUV is a rhombus and NPQR is a parallelogram. ∠RSU = 78° and ∠QRS = 91°.
- Find ∠MRN
- Find ∠RQP
(a)
∠UVR = ∠USR = 78°
∠VRU
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠MRN
= 90° - 51°
= 39°
(b)
∠NRQ
= 360° - 91° - 90° - 51°
= 128° (Angles at a point)
∠PQR
= 180° - 128°
= 52° (Interior Angles, NR//PF)
Answer(s): (a) 39°; (b) 52°