The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 102°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 102°
∠PTU = 102° (Corresponding angles)
∠STP
= 180° - 102°
= 78° (Angles on a straight line)
∠GPH
= 180° - 78° - 78°
= 24° (Isosceles triangle)
(b)
∠STP = ∠GHP = 78° (Corresponding angles)
∠PHK
= 180° - 78°
= 102° (Angles on a straight line)
∠HKU
= (180° - 102°) ÷ 2
= 39° (Isosceles triangle)
∠LKP
= 180° - 39°
= 141° (Angles on a straight line)
Answer(s): (a) 24°; (b) 141°