The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 113°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 113°
∠SVX = 113° (Corresponding angles)
∠UVS
= 180° - 113°
= 67° (Angles on a straight line)
∠KSL
= 180° - 67° - 67°
= 46° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 67° (Corresponding angles)
∠SLN
= 180° - 67°
= 113° (Angles on a straight line)
∠LNX
= (180° - 113°) ÷ 2
= 33.5° (Isosceles triangle)
∠PNS
= 180° - 33.5°
= 146.5° (Angles on a straight line)
Answer(s): (a) 46°; (b) 146.5°