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In figure, state if AB || EF is true or false?

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True

False

answer is A.

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Detailed Solution

It is given that we have to find if “AB∥EF” is true or false.
Question Image

We can observe from the figure that,

∠ A C D = ∠ A C E + ∠ E C D

We can substitute the value from the figure in the above equation,

⇒ ∠ A C D = 35 ° + 22 °

⇒ ∠ A C D = 57 °

⇒ ∠ B A C = 57 °

We can observe that lines

B A

and CD are intersected by the line

A C

such that,

∠ A C D = ∠ B A C

.
So, the alternate angles are equal.
We can also observe that,

A B ∥ C D

...... (1)
We can also observe that ∠ECD and ∠CEF are located in the interior side of the transversal.
Hence, we can write that,

∠ E C D + ∠ C E F = 35 ° + 145 °

⇒ ∠ E C D + ∠ C E F = 180 °

We know that, sum of the angles of the interior angles on the same side of the transversal CE is

180 °

.
So, they are supplementary angles.
We can observe that,

E F ∥ C D

...... (2)
From both equation 1 and 2, we can write that

A B ∥ E F

.
It is verified that

A B ∥ E F

.
Hence, the correct option is 1.

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