The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 110°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 110°
∠PTU = 110° (Corresponding angles)
∠STP
= 180° - 110°
= 70° (Angles on a straight line)
∠GPH
= 180° - 70° - 70°
= 40° (Isosceles triangle)
(b)
∠STP = ∠GHP = 70° (Corresponding angles)
∠PHK
= 180° - 70°
= 110° (Angles on a straight line)
∠HKU
= (180° - 110°) ÷ 2
= 35° (Isosceles triangle)
∠LKP
= 180° - 35°
= 145° (Angles on a straight line)
Answer(s): (a) 40°; (b) 145°