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Lines And Angles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsLines And Angles3 Marks
Question
In figure, PQ || AB and PR || BC. If $\angle\text{QPR}=102^\circ,$ determine $\angle\text{ABC}.$ Give reasons.
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Answer

AB is produce to meet PR at K Since PQ || AB$\angle\text{QPR}=\angle\text{BKR}=102^\circ$[corresponding angles]
Since PR ∥ BC$\angle\text{RKB}+\angle\text{CBK}=180^\circ$[Since Corresponding angles are supplementary]
$\angle\text{CKB}=180-102=78$
$\therefore\ \angle\text{CKB}=78^\circ$

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