Question

 In the below, PQ || AB and PR || BC. If `∠`QPR = 102°, determine `∠`ABC. Give reasons.

Answer 1

AB is produce to meet PR at K

Since PQ || AB 

`∠`QPR = `∠`BGR = 102°  ...[corresponding angles]

Since PR || BC

∴`∠`RGB + `∠`CBG = 180°        ...[Corresponding angles are supplementary]

⇒ `∠`CBG =180° - 102° = 78°

∴ `∠`CBG = `∠` ABC

`∠` ABC = 78°.