The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 120°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 120°
∠PTU = 120° (Corresponding angles)
∠STP
= 180° - 120°
= 60° (Angles on a straight line)
∠GPH
= 180° - 60° - 60°
= 60° (Isosceles triangle)
(b)
∠STP = ∠GHP = 60° (Corresponding angles)
∠PHK
= 180° - 60°
= 120° (Angles on a straight line)
∠HKU
= (180° - 120°) ÷ 2
= 30° (Isosceles triangle)
∠LKP
= 180° - 30°
= 150° (Angles on a straight line)
Answer(s): (a) 60°; (b) 150°