The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 106°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 106°
∠PTU = 106° (Corresponding angles)
∠STP
= 180° - 106°
= 74° (Angles on a straight line)
∠GPH
= 180° - 74° - 74°
= 32° (Isosceles triangle)
(b)
∠STP = ∠GHP = 74° (Corresponding angles)
∠PHK
= 180° - 74°
= 106° (Angles on a straight line)
∠HKU
= (180° - 106°) ÷ 2
= 37° (Isosceles triangle)
∠LKP
= 180° - 37°
= 143° (Angles on a straight line)
Answer(s): (a) 32°; (b) 143°