The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 102°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 102°
∠SVX = 102° (Corresponding angles)
∠UVS
= 180° - 102°
= 78° (Angles on a straight line)
∠KSL
= 180° - 78° - 78°
= 24° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 78° (Corresponding angles)
∠SLN
= 180° - 78°
= 102° (Angles on a straight line)
∠LNX
= (180° - 102°) ÷ 2
= 39° (Isosceles triangle)
∠PNS
= 180° - 39°
= 141° (Angles on a straight line)
Answer(s): (a) 24°; (b) 141°