For what value of $x+y$ in the figure will $ABC$ be a straight line? Justify your answer.
(N/A) In the given figure,$x$ and $y$ are two adjacent angles formed at point $B$.
For $ABC$ to be a straight line,the sum of the adjacent angles $x$ and $y$ must be equal to $180^{\circ}$.
This is based on the linear pair axiom,which states that if a ray stands on a line,then the sum of two adjacent angles so formed is $180^{\circ}$.
Therefore,$x + y = 180^{\circ}$.
For $ABC$ to be a straight line,the sum of the adjacent angles $x$ and $y$ must be equal to $180^{\circ}$.
This is based on the linear pair axiom,which states that if a ray stands on a line,then the sum of two adjacent angles so formed is $180^{\circ}$.
Therefore,$x + y = 180^{\circ}$.
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