MCQ

AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of ∠FEB. If ∠LEB = 35°, then ∠CFQ will be

#### Options

55°

70°

110°

130°

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#### Solution

The figure is given as follows:

It is given that, AB || CDwith PQ as transversal.

Also, EL is the bisector∠BEF and∠LEB = 35°.

We need to find∠CFQ.

Since, EL is the bisector∠BEFand ∠LEB = 35°.

Therefore,

∠BEF = 2(∠LEB)

∠BEF = 2(35°)

∠BEF = 70° (1)

We have AB|| CD, the ∠BEF and ∠DFE are consecutive interior angles, which must be supplementary.

∠BEF + ∠DFE = 180°

From equation (i), we get:

70° + ∠DFE = 180°

∠DFE = 180° - 70°

∠DFE = 110° ........(2)

We have and as vertically opposite angles.

Therefore,

∠CFQ = ∠DFE

∠CFQ = 110°

Concept: Parallel Lines and a Transversal

Is there an error in this question or solution?

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