AB and CD are two parallel lines, PQ cuts AB and CD at E and F respectively. EL is the bisector of `angleBEF`. If `angleLEB=35^(@)` then `angleCFQ` will be :

Options

A. `70^(@)`
B. `55^(@)`
C. `110^(@)`
D. `125^(@)`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Given Information
We have two parallel lines AB and CD, and a transversal PQ that intersects these lines at points E and F respectively. The angle bisector EL divides angle BEF into two equal parts. We know that angle LEB = 35°.

**Hint:** Identify the relationships between the angles formed by the transversal and the parallel lines.

### Step 2: Determine Angle LEF
Since EL is the angle bisector of angle BEF, we can conclude that angle LEF is also equal to angle LEB. Therefore, angle LEF = 35°.

**Hint:** Remember that an angle bisector divides an angle into two equal parts.

### Step 3: Calculate Angle BEF
Now, we can find angle BEF. Since angle BEF is composed of angle LEB and angle LEF:
\[ \text{Angle BEF} = \text{Angle LEB} + \text{Angle LEF} = 35° + 35° = 70°. \]

**Hint:** Use the property of angle bisectors to find the total angle.

### Step 4: Use the Parallel Lines Property
Since AB and CD are parallel lines, angle BEF is equal to angle CFE (by the Alternate Interior Angles Theorem). Therefore:
\[ \text{Angle CFE} = \text{Angle BEF} = 70°. \]

**Hint:** Recall that alternate interior angles are equal when two lines are parallel.

### Step 5: Set Up the Equation for Straight Line PQ
Since PQ is a straight line, the sum of angles CFE and CFQ must equal 180°:
\[ \text{Angle CFE} + \text{Angle CFQ} = 180°. \]

**Hint:** Remember that the angles on a straight line sum up to 180°.

### Step 6: Solve for Angle CFQ
Substituting the known value of angle CFE into the equation:
\[ 70° + \text{Angle CFQ} = 180°. \]
Now, isolate angle CFQ:
\[ \text{Angle CFQ} = 180° - 70° = 110°. \]

**Hint:** Perform simple arithmetic to find the unknown angle.

### Conclusion
Thus, the measure of angle CFQ is 110°.

**Final Answer:** Angle CFQ = 110°.