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Question
For what value of x + y in figure will ABC be a line? Justify your answer.
Solution
The value of x + y should be 180° for ABC to be a line.
Justification:
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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