The figure is not drawn to scale. KNPR is a parallelogram, HKR and KLR are isosceles triangles. RP//SY and ∠PXY= 111°. HN is straight line.
- Find ∠HRK.
- Find ∠NLR.
(a)
∠PXY = 111°
∠RUV = 111° (Corresponding angles)
∠TUR
= 180° - 111°
= 69° (Angles on a straight line)
∠HRK
= 180° - 69° - 69°
= 42° (Isosceles triangle)
(b)
∠TUR = ∠HKR = 69° (Corresponding angles)
∠RKL
= 180° - 69°
= 111° (Angles on a straight line)
∠KLV
= (180° - 111°) ÷ 2
= 34.5° (Isosceles triangle)
∠NLR
= 180° - 34.5°
= 145.5° (Angles on a straight line)
Answer(s): (a) 42°; (b) 145.5°