The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 120°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 120°
∠RUV = 120° (Corresponding angles)
∠TUR
= 180° - 120°
= 60° (Angles on a straight line)
∠HRK
= 180° - 60° - 60°
= 60° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 60° (Corresponding angles)
∠RKL
= 180° - 60°
= 120° (Angles on a straight line)
∠KLV
= (180° - 120°) ÷ 2
= 30° (Isosceles triangle)
∠NLR
= 180° - 30°
= 150° (Angles on a straight line)
Answer(s): (a) 60°; (b) 150°