The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 109°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 109°
∠SVX = 109° (Corresponding angles)
∠UVS
= 180° - 109°
= 71° (Angles on a straight line)
∠KSL
= 180° - 71° - 71°
= 38° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 71° (Corresponding angles)
∠SLN
= 180° - 71°
= 109° (Angles on a straight line)
∠LNX
= (180° - 109°) ÷ 2
= 35.5° (Isosceles triangle)
∠PNS
= 180° - 35.5°
= 144.5° (Angles on a straight line)
Answer(s): (a) 38°; (b) 144.5°