Since AB // CD and AB // EF, then CD // EF. Therefore, angles AEC and CED are alternate interior angles and are equal. Since angle CED = 105 degrees, then angle AEC = 105 degrees. Similarly, AB // EF and AB // CD, then CD // EF. Therefore, angles ACE and CED are corresponding angles and are congruent. Since angle CED = 95 degrees, then angle ACE = 95 degrees.
Since AB // CD and AB // EF, then CD // EF.
This means that lines AB and EF are parallel to line CD.
When a transversal intersects two parallel lines, the alternate interior angles are equal.
Alternate interior angles are angles that lie on opposite sides of the transversal and on the same side of the parallel lines.
In the given figure, angles AEC and CED are alternate interior angles.
Therefore, angles AEC and CED are equal.
Angle CED is given as 105 degrees.
Therefore, angle AEC is also equal to 105 degrees.
AEC = 105 degrees
Question 11: ACE = 95 degrees
Since AB // CD and AB // EF, then CD // EF.
This means that lines AB and EF are parallel to line CD.
When a transversal intersects two parallel lines, the corresponding angles are equal.
Corresponding angles are angles that lie on the same side of the transversal and on the same side of the parallel lines.
In the given figure, angles ACE and CED are corresponding angles. Therefore, angles ACE and CED are equal.
Angle CED is given as 95 degrees.
Therefore, angle ACE is also equal to 95 degrees.
ACE = 95 degrees
The concept of alternate interior angles and corresponding angles is important in geometry because it allows us to solve for unknown angle measures.
For example, if we know that two lines are parallel and we are given the measure of one alternate interior angle, then we can find the measure of the other alternate interior angle.
Similarly, if we know that two lines are parallel and we are given the measure of one corresponding angle, then we can find the measure of the other corresponding angle.