The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 107°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 107°
∠RUV = 107° (Corresponding angles)
∠TUR
= 180° - 107°
= 73° (Angles on a straight line)
∠HRK
= 180° - 73° - 73°
= 34° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 73° (Corresponding angles)
∠RKL
= 180° - 73°
= 107° (Angles on a straight line)
∠KLV
= (180° - 107°) ÷ 2
= 36.5° (Isosceles triangle)
∠NLR
= 180° - 36.5°
= 143.5° (Angles on a straight line)
Answer(s): (a) 34°; (b) 143.5°