In the figure, KNRU is a rectangle, RSUV is a rhombus and NPQR is a parallelogram. ∠RSU = 76° and ∠QRS = 97°.
- Find ∠MRN
- Find ∠RQP
(a)
∠UVR = ∠USR = 76°
∠VRU
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠MRN
= 90° - 52°
= 38°
(b)
∠NRQ
= 360° - 97° - 90° - 52°
= 121° (Angles at a point)
∠PQR
= 180° - 121°
= 59° (Interior Angles, NR//PF)
Answer(s): (a) 38°; (b) 59°