The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 101°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 101°
∠SVX = 101° (Corresponding angles)
∠UVS
= 180° - 101°
= 79° (Angles on a straight line)
∠KSL
= 180° - 79° - 79°
= 22° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 79° (Corresponding angles)
∠SLN
= 180° - 79°
= 101° (Angles on a straight line)
∠LNX
= (180° - 101°) ÷ 2
= 39.5° (Isosceles triangle)
∠PNS
= 180° - 39.5°
= 140.5° (Angles on a straight line)
Answer(s): (a) 22°; (b) 140.5°