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