The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 105°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 105°
∠SVX = 105° (Corresponding angles)
∠UVS
= 180° - 105°
= 75° (Angles on a straight line)
∠KSL
= 180° - 75° - 75°
= 30° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 75° (Corresponding angles)
∠SLN
= 180° - 75°
= 105° (Angles on a straight line)
∠LNX
= (180° - 105°) ÷ 2
= 37.5° (Isosceles triangle)
∠PNS
= 180° - 37.5°
= 142.5° (Angles on a straight line)
Answer(s): (a) 30°; (b) 142.5°