The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 104°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 104°
∠PTU = 104° (Corresponding angles)
∠STP
= 180° - 104°
= 76° (Angles on a straight line)
∠GPH
= 180° - 76° - 76°
= 28° (Isosceles triangle)
(b)
∠STP = ∠GHP = 76° (Corresponding angles)
∠PHK
= 180° - 76°
= 104° (Angles on a straight line)
∠HKU
= (180° - 104°) ÷ 2
= 38° (Isosceles triangle)
∠LKP
= 180° - 38°
= 142° (Angles on a straight line)
Answer(s): (a) 28°; (b) 142°