The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 113°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 113°
∠RUV = 113° (Corresponding angles)
∠TUR
= 180° - 113°
= 67° (Angles on a straight line)
∠HRK
= 180° - 67° - 67°
= 46° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 67° (Corresponding angles)
∠RKL
= 180° - 67°
= 113° (Angles on a straight line)
∠KLV
= (180° - 113°) ÷ 2
= 33.5° (Isosceles triangle)
∠NLR
= 180° - 33.5°
= 146.5° (Angles on a straight line)
Answer(s): (a) 46°; (b) 146.5°
