The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 106°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 106°
∠RUV = 106° (Corresponding angles)
∠TUR
= 180° - 106°
= 74° (Angles on a straight line)
∠HRK
= 180° - 74° - 74°
= 32° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 74° (Corresponding angles)
∠RKL
= 180° - 74°
= 106° (Angles on a straight line)
∠KLV
= (180° - 106°) ÷ 2
= 37° (Isosceles triangle)
∠NLR
= 180° - 37°
= 143° (Angles on a straight line)
Answer(s): (a) 32°; (b) 143°