The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 101°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 101°
∠RUV = 101° (Corresponding angles)
∠TUR
= 180° - 101°
= 79° (Angles on a straight line)
∠HRK
= 180° - 79° - 79°
= 22° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 79° (Corresponding angles)
∠RKL
= 180° - 79°
= 101° (Angles on a straight line)
∠KLV
= (180° - 101°) ÷ 2
= 39.5° (Isosceles triangle)
∠NLR
= 180° - 39.5°
= 140.5° (Angles on a straight line)
Answer(s): (a) 22°; (b) 140.5°