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For what value of $x + y$ in figure, will ABC be a line?

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x + y = 120 o

x + y = 150 o

x + y = 160 o

x + y = 180 o

answer is D.

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Detailed Solution

Given,

We know that two angles are said to be adjacent if they have a common side and vertex.
According to the given figure,

∠ C B D = x

and

∠ A B D = y

∠ C B D

and

∠ A B D

are adjacent angles as they share a common side BD and a common vertex B.
Since, the sum of the adjacent angles on a straight line is

180 o

,
ABC is a straight line if

∠ A B D + ∠ C B D = 180 o

i.e.,
if

x + y = 180 o

.
Hence, ABC forms a straight line if

x + y = 180 o

.
Thus, ABC is a straight line if the value of

x + y

is equal to

180 °

.
Therefore, option (4) is correct.

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