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In the figure given below, let BA and DC are two parallel lines such that QP cuts BA and DC at E and F respectively. If LE is a bisector of $∠ F E B$ such that $∠ L E B = 35 °,$ such that then what is the measure of $∠ C F Q$ then what is the measure of ?

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70 °

110 °

130 °

140 °

answer is B.

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Detailed Solution

It is given that BA and DC are two parallel lines such that QP cuts BA and DC at E and F respectively.
Since LE is a bisector of

∠ F E B

such that

∠ L E B = 35 °,

therefore we have,

∠ F E B = 2 ∠ L E B ⇒ ∠ F E B = 2 × 35 ° ⇒ ∠ F E B = 70 °

Since BA and DC are two parallel lines with PQ as a transversal, therefore using the property of co-interior angles, we have,

∠ F E B + ∠ E F D = 180 °

⇒ 70 ° + ∠ E F D = 180 ° ⇒ ∠ E F D = 110 °

Using the vertically opposite angles property, we have,

∠ C F Q = ∠ E F D ⇒ ∠ C F Q = ∠ 110 °

Therefore, the measure of

∠ C F Q = 110 ° .

Hence, option (2) is correct.

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