The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 108°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 108°
∠RUV = 108° (Corresponding angles)
∠TUR
= 180° - 108°
= 72° (Angles on a straight line)
∠HRK
= 180° - 72° - 72°
= 36° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 72° (Corresponding angles)
∠RKL
= 180° - 72°
= 108° (Angles on a straight line)
∠KLV
= (180° - 108°) ÷ 2
= 36° (Isosceles triangle)
∠NLR
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 36°; (b) 144°