The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 108°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 108°
∠PTU = 108° (Corresponding angles)
∠STP
= 180° - 108°
= 72° (Angles on a straight line)
∠GPH
= 180° - 72° - 72°
= 36° (Isosceles triangle)
(b)
∠STP = ∠GHP = 72° (Corresponding angles)
∠PHK
= 180° - 72°
= 108° (Angles on a straight line)
∠HKU
= (180° - 108°) ÷ 2
= 36° (Isosceles triangle)
∠LKP
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 36°; (b) 144°