The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 118°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 118°
∠RUV = 118° (Corresponding angles)
∠TUR
= 180° - 118°
= 62° (Angles on a straight line)
∠HRK
= 180° - 62° - 62°
= 56° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 62° (Corresponding angles)
∠RKL
= 180° - 62°
= 118° (Angles on a straight line)
∠KLV
= (180° - 118°) ÷ 2
= 31° (Isosceles triangle)
∠NLR
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 56°; (b) 149°