The figure is not drawn to scale. HLNP is a parallelogram, GHP and HKP are isosceles triangles. PN//RX and ∠NVX= 111°. GL is straight line.
- Find ∠GPH.
- Find ∠LKP.
(a)
∠NVX = 111°
∠PTU = 111° (Corresponding angles)
∠STP
= 180° - 111°
= 69° (Angles on a straight line)
∠GPH
= 180° - 69° - 69°
= 42° (Isosceles triangle)
(b)
∠STP = ∠GHP = 69° (Corresponding angles)
∠PHK
= 180° - 69°
= 111° (Angles on a straight line)
∠HKU
= (180° - 111°) ÷ 2
= 34.5° (Isosceles triangle)
∠LKP
= 180° - 34.5°
= 145.5° (Angles on a straight line)
Answer(s): (a) 42°; (b) 145.5°