Question

For what value of $x+y$ in Figure will $ABC$ be a line? Justify your answer.

Answer 1

Calculate the required angle:

From the given diagram we note that

$BD$ is a ray that intersects $AB$ and $BC$ at the point $B$ which results in

$\angle ABD=y$

and, $\angle DBC=x$

From the linear pair of axiom, we know that if a ray stands on a line, then the sum of two adjacent angles so formed is $180°$.

If the sum of two adjacent angles is $180°$, then a ray stands on a line.

Thus, for $ABC$ to be a line,

The sum of $\angle ABD$ and $\angle DBC$ should be equal to $180°$.

$\therefore \angle ABD+\angle DBC=180°$

$\Rightarrow$ $x+y=180°$

Therefore, the value of $x+y$ should be equal to $180°$ for $ABC$ to be a line.