The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 103°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 103°
∠SVX = 103° (Corresponding angles)
∠UVS
= 180° - 103°
= 77° (Angles on a straight line)
∠KSL
= 180° - 77° - 77°
= 26° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 77° (Corresponding angles)
∠SLN
= 180° - 77°
= 103° (Angles on a straight line)
∠LNX
= (180° - 103°) ÷ 2
= 38.5° (Isosceles triangle)
∠PNS
= 180° - 38.5°
= 141.5° (Angles on a straight line)
Answer(s): (a) 26°; (b) 141.5°