The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 110°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 110°
∠RUV = 110° (Corresponding angles)
∠TUR
= 180° - 110°
= 70° (Angles on a straight line)
∠HRK
= 180° - 70° - 70°
= 40° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 70° (Corresponding angles)
∠RKL
= 180° - 70°
= 110° (Angles on a straight line)
∠KLV
= (180° - 110°) ÷ 2
= 35° (Isosceles triangle)
∠NLR
= 180° - 35°
= 145° (Angles on a straight line)
Answer(s): (a) 40°; (b) 145°