The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 114°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 114°
∠PTU = 114° (Corresponding angles)
∠STP
= 180° - 114°
= 66° (Angles on a straight line)
∠GPH
= 180° - 66° - 66°
= 48° (Isosceles triangle)
(b)
∠STP = ∠GHP = 66° (Corresponding angles)
∠PHK
= 180° - 66°
= 114° (Angles on a straight line)
∠HKU
= (180° - 114°) ÷ 2
= 33° (Isosceles triangle)
∠LKP
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 48°; (b) 147°