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In the figure given below, if AB || CD and CD || EF then what is the measure of $∠ A C E$ ?

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30 °

45 °

20 °

65 °

answer is C.

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Detailed Solution

It is given that AB || CD and CD || EF.
Consider the transversal EC over the parallel lines CD and EF.
Therefore,

∠ E C D

and

∠ C E F

are interior angles and their sum total should be equal to

180 ° .

∴ ∠ E C D + ∠ C E F = 180 ° ⇒ ∠ E C D + 130 ° = 180 °

⇒ ∠ E C D = 50 °

Consider the transversal AC over the parallel lines AB and CD.
Therefore,

∠ C A B

and

∠ A C D

are alternate interior angles which means that they are equal.

∴ ∠ A C D = ∠ C A B = 70 °

Observe that also

∠ A C D

is equal to the sum total of

∠ A C E

and

∠ E C D .

∴ ∠ A C E + ∠ E C D = ∠ A C D ⇒ ∠ A C E + 50 ° = 70 ° ⇒ ∠ A C E = 20 °

Therefore, the measure of

∠ A C E = 20 ° .

Hence, option (3) is correct.

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