The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 113°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 113°
∠PTU = 113° (Corresponding angles)
∠STP
= 180° - 113°
= 67° (Angles on a straight line)
∠GPH
= 180° - 67° - 67°
= 46° (Isosceles triangle)
(b)
∠STP = ∠GHP = 67° (Corresponding angles)
∠PHK
= 180° - 67°
= 113° (Angles on a straight line)
∠HKU
= (180° - 113°) ÷ 2
= 33.5° (Isosceles triangle)
∠LKP
= 180° - 33.5°
= 146.5° (Angles on a straight line)
Answer(s): (a) 46°; (b) 146.5°