The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 107°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 107°
∠PTU = 107° (Corresponding angles)
∠STP
= 180° - 107°
= 73° (Angles on a straight line)
∠GPH
= 180° - 73° - 73°
= 34° (Isosceles triangle)
(b)
∠STP = ∠GHP = 73° (Corresponding angles)
∠PHK
= 180° - 73°
= 107° (Angles on a straight line)
∠HKU
= (180° - 107°) ÷ 2
= 36.5° (Isosceles triangle)
∠LKP
= 180° - 36.5°
= 143.5° (Angles on a straight line)
Answer(s): (a) 34°; (b) 143.5°