The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 104°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 104°
∠RUV = 104° (Corresponding angles)
∠TUR
= 180° - 104°
= 76° (Angles on a straight line)
∠HRK
= 180° - 76° - 76°
= 28° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 76° (Corresponding angles)
∠RKL
= 180° - 76°
= 104° (Angles on a straight line)
∠KLV
= (180° - 104°) ÷ 2
= 38° (Isosceles triangle)
∠NLR
= 180° - 38°
= 142° (Angles on a straight line)
Answer(s): (a) 28°; (b) 142°