The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 104°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 104°
∠SVX = 104° (Corresponding angles)
∠UVS
= 180° - 104°
= 76° (Angles on a straight line)
∠KSL
= 180° - 76° - 76°
= 28° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 76° (Corresponding angles)
∠SLN
= 180° - 76°
= 104° (Angles on a straight line)
∠LNX
= (180° - 104°) ÷ 2
= 38° (Isosceles triangle)
∠PNS
= 180° - 38°
= 142° (Angles on a straight line)
Answer(s): (a) 28°; (b) 142°