The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 110°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 110°
∠SVX = 110° (Corresponding angles)
∠UVS
= 180° - 110°
= 70° (Angles on a straight line)
∠KSL
= 180° - 70° - 70°
= 40° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 70° (Corresponding angles)
∠SLN
= 180° - 70°
= 110° (Angles on a straight line)
∠LNX
= (180° - 110°) ÷ 2
= 35° (Isosceles triangle)
∠PNS
= 180° - 35°
= 145° (Angles on a straight line)
Answer(s): (a) 40°; (b) 145°