For what value of x + y in Fig. 6.4 will ABC be a line? Justify your answer.


From the figure we can say that,


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


ABD = y


and, DBC = x


We know,


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 ABD and DBC should be equal to 180°.


ABD + DBC = 180°


x + y = 180°


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


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