The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 109°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 109°
∠PTU = 109° (Corresponding angles)
∠STP
= 180° - 109°
= 71° (Angles on a straight line)
∠GPH
= 180° - 71° - 71°
= 38° (Isosceles triangle)
(b)
∠STP = ∠GHP = 71° (Corresponding angles)
∠PHK
= 180° - 71°
= 109° (Angles on a straight line)
∠HKU
= (180° - 109°) ÷ 2
= 35.5° (Isosceles triangle)
∠LKP
= 180° - 35.5°
= 144.5° (Angles on a straight line)
Answer(s): (a) 38°; (b) 144.5°