The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 114°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 114°
∠RUV = 114° (Corresponding angles)
∠TUR
= 180° - 114°
= 66° (Angles on a straight line)
∠HRK
= 180° - 66° - 66°
= 48° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 66° (Corresponding angles)
∠RKL
= 180° - 66°
= 114° (Angles on a straight line)
∠KLV
= (180° - 114°) ÷ 2
= 33° (Isosceles triangle)
∠NLR
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 48°; (b) 147°