Question

 In the below, PQ || AB and PR || BC. If ${\displaystyle \angle }$QPR = 102°, determine ${\displaystyle \angle }$ABC. Give reasons.

Answer 1

AB is produce to meet PR at K

Since PQ || AB 

${\displaystyle \angle }$QPR = ${\displaystyle \angle }$BGR = 102°  ...[corresponding angles]

Since PR || BC

∴${\displaystyle \angle }$RGB + ${\displaystyle \angle }$CBG = 180°        ...[Corresponding angles are supplementary]

⇒ ${\displaystyle \angle }$CBG =180° - 102° = 78°

∴ ${\displaystyle \angle }$CBG = ${\displaystyle \angle }$ ABC

${\displaystyle \angle }$ ABC = 78°.