The figure is not drawn to scale. LPRS is a parallelogram, KLS and LNS are isosceles triangles. SR//TZ and ∠RYZ= 115°. KP is straight line.
- Find ∠KSL.
- Find ∠PNS.
(a)
∠RYZ = 115°
∠SVX = 115° (Corresponding angles)
∠UVS
= 180° - 115°
= 65° (Angles on a straight line)
∠KSL
= 180° - 65° - 65°
= 50° (Isosceles triangle)
(b)
∠UVS = ∠KLS = 65° (Corresponding angles)
∠SLN
= 180° - 65°
= 115° (Angles on a straight line)
∠LNX
= (180° - 115°) ÷ 2
= 32.5° (Isosceles triangle)
∠PNS
= 180° - 32.5°
= 147.5° (Angles on a straight line)
Answer(s): (a) 50°; (b) 147.5°