The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 100°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 100°
∠RUV = 100° (Corresponding angles)
∠TUR
= 180° - 100°
= 80° (Angles on a straight line)
∠HRK
= 180° - 80° - 80°
= 20° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 80° (Corresponding angles)
∠RKL
= 180° - 80°
= 100° (Angles on a straight line)
∠KLV
= (180° - 100°) ÷ 2
= 40° (Isosceles triangle)
∠NLR
= 180° - 40°
= 140° (Angles on a straight line)
Answer(s): (a) 20°; (b) 140°