The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 111°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 111°
∠SVX = 111° (Corresponding angles)
∠UVS
= 180° - 111°
= 69° (Angles on a straight line)
∠KSL
= 180° - 69° - 69°
= 42° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 69° (Corresponding angles)
∠SLN
= 180° - 69°
= 111° (Angles on a straight line)
∠LNX
= (180° - 111°) ÷ 2
= 34.5° (Isosceles triangle)
∠PNS
= 180° - 34.5°
= 145.5° (Angles on a straight line)
Answer(s): (a) 42°; (b) 145.5°
