ABCD is a quadrilateral in which angle ABC = 73°, angle C = 97°, angle D =110° if AE is parallel to DC & BE is parallel to AD & AE intersects BC at F find the measure of angle EBF

Angle EBF=27

Hope my answer helps you

To find the measure of angle EBF, we can start by using the fact that AE is parallel to DC and BE is parallel to AD. This tells us that angle ABC and angle AED are alternate interior angles and are congruent.

So, angle ABC = angle AED = 73°.

Next, we can use the fact that angle D = 110° and angle C = 97° to find angle BCD. To do this, we can subtract angle D and angle C from 180° since the sum of angles in a quadrilateral is 360°.

180° - 110° - 97° = 73°.

Therefore, angle BCD = 73°.

Now, since AE intersects BC at F, we can use the angle sum property of triangles to find angle EBF. The sum of angles in a triangle is 180°.

angle EBF + angle B + angle F = 180°.

We know that angle BCD = 73° and angle B = angle ABC = 73°.

Let's substitute these values into the equation:

angle EBF + 73° + angle F = 180°.

Rearranging the equation, we have:

angle EBF + angle F = 180° - 73° = 107°.

Since angle F = angle EBF (as they are corresponding angles formed by parallel lines AE and DC), we can rewrite the equation as:

2 * angle EBF = 107°.

Dividing both sides of the equation by 2, we get:

angle EBF = 107° / 2 = 53.5°.

Therefore, the measure of angle EBF is 53.5°.

To find the measure of angle EBF, we can use the property of alternate interior angles formed by parallel lines. Here's how you can do it:

1. Start by drawing a rough sketch of the given quadrilateral ABCD. Label the angles as stated in the question (ABC = 73°, C = 97°, D = 110°).

2. According to the question, AE is parallel to DC and BE is parallel to AD. Therefore, angle ABC and angle EBF are alternate interior angles, as they are on opposite sides of the line AB and are between the parallel lines AE and DC.

3. Since alternate interior angles are congruent when the lines intersected by the transversal (in this case, AE) are parallel, we have angle ABC = angle EBF.

4. Since we know the measure of angle ABC is 73°, angle EBF also has a measure of 73°.

Therefore, the measure of angle EBF is 73°.

The answer to this question is 27°.