The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 118°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 118°
∠PTU = 118° (Corresponding angles)
∠STP
= 180° - 118°
= 62° (Angles on a straight line)
∠GPH
= 180° - 62° - 62°
= 56° (Isosceles triangle)
(b)
∠STP = ∠GHP = 62° (Corresponding angles)
∠PHK
= 180° - 62°
= 118° (Angles on a straight line)
∠HKU
= (180° - 118°) ÷ 2
= 31° (Isosceles triangle)
∠LKP
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 56°; (b) 149°