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In the given figure, $l ‖ m .$ If $s$ and $t$ be transversals such that $s$ is not parallel to t, the values of x and y are:

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x =

130 o

and y =

115 o

x =

130 o

and y =

215 o

x =

135 o

and y =

115 o

x =

130 o

and y =

105 o

answer is A.

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Detailed Solution

Given a figure.
Question Image

Angles on the same side of a transverse are equal.
So,

∠ 3 = ∠ 1 ⇒ ∠ 1 = 50 o

Now, sum of angles on a straight line is supplementary.

∠ 1 + x = 180 o 50 o + x = 180 o x = 180 o − 50 o x = 130 o

Now, as line t is transversal on-line l and m,

∠ 4 = ∠ 2 ⇒ ∠ 2 = 65 o

Now, the sum of angles on a straight line is supplementary.

∠ 2 + y = 180 o 65 o + y = 180 o y = 180 o − 65 o y = 115 o

Therefore, x =

130 o

and y =

115 o

.
Hence, option 1 is correct.

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In the given figure, l‖m. If s and t be transversals such that s is not parallel to t, the values of x and y are:

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In the given figure, $l ‖ m .$ If $s$ and $t$ be transversals such that $s$ is not parallel to t, the values of x and y are: