The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 103°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 103°
∠RUV = 103° (Corresponding angles)
∠TUR
= 180° - 103°
= 77° (Angles on a straight line)
∠HRK
= 180° - 77° - 77°
= 26° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 77° (Corresponding angles)
∠RKL
= 180° - 77°
= 103° (Angles on a straight line)
∠KLV
= (180° - 103°) ÷ 2
= 38.5° (Isosceles triangle)
∠NLR
= 180° - 38.5°
= 141.5° (Angles on a straight line)
Answer(s): (a) 26°; (b) 141.5°