The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 119°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 119°
∠RUV = 119° (Corresponding angles)
∠TUR
= 180° - 119°
= 61° (Angles on a straight line)
∠HRK
= 180° - 61° - 61°
= 58° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 61° (Corresponding angles)
∠RKL
= 180° - 61°
= 119° (Angles on a straight line)
∠KLV
= (180° - 119°) ÷ 2
= 30.5° (Isosceles triangle)
∠NLR
= 180° - 30.5°
= 149.5° (Angles on a straight line)
Answer(s): (a) 58°; (b) 149.5°