The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 106°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 106°
∠SVX = 106° (Corresponding angles)
∠UVS
= 180° - 106°
= 74° (Angles on a straight line)
∠KSL
= 180° - 74° - 74°
= 32° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 74° (Corresponding angles)
∠SLN
= 180° - 74°
= 106° (Angles on a straight line)
∠LNX
= (180° - 106°) ÷ 2
= 37° (Isosceles triangle)
∠PNS
= 180° - 37°
= 143° (Angles on a straight line)
Answer(s): (a) 32°; (b) 143°