In the figure, $PQ \parallel AB$ and $PR \parallel BC$. If $\angle QPR = 102^o$. Determine $\angle ABC$. Give reasons."

Given:

$PQ \parallel AB$ and $PR \parallel BC$.

$\angle QPR = 102^o$.

To do:

We have to determine $\angle ABC$.

Solution:

Produce $BA$ to meet $PR$ at $D$.

$PQ \parallel AB$

This implies,

$PQ \parallel DB$

Therefore,

$\angle QPR = \angle ADR$                 (Corresponding angles)

$\angle ADR = \angle BDR = 102^o$

$\angle BDR + \angle DBC = 180^o$             (Sum of co-interior angles)

$102^o + \angle DBC = 180^o$

$\angle DBC = 180^o - 102^o$

$\angle DBC = 78^o$

This implies,

$\angle ABC = 78^o$.

Hence, $\angle ABC = 78^o$.

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Updated on: 10-Oct-2022

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