The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 118°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 118°
∠SVX = 118° (Corresponding angles)
∠UVS
= 180° - 118°
= 62° (Angles on a straight line)
∠KSL
= 180° - 62° - 62°
= 56° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 62° (Corresponding angles)
∠SLN
= 180° - 62°
= 118° (Angles on a straight line)
∠LNX
= (180° - 118°) ÷ 2
= 31° (Isosceles triangle)
∠PNS
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 56°; (b) 149°