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Question
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°
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°
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