The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 115°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 115°
∠PTU = 115° (Corresponding angles)
∠STP
= 180° - 115°
= 65° (Angles on a straight line)
∠GPH
= 180° - 65° - 65°
= 50° (Isosceles triangle)
(b)
∠STP = ∠GHP = 65° (Corresponding angles)
∠PHK
= 180° - 65°
= 115° (Angles on a straight line)
∠HKU
= (180° - 115°) ÷ 2
= 32.5° (Isosceles triangle)
∠LKP
= 180° - 32.5°
= 147.5° (Angles on a straight line)
Answer(s): (a) 50°; (b) 147.5°
