Find the measure of angle AEF

Question

in the figure below. Enter only the number.

An image shows that line AB passes through points A, E, and B. Line CD passes through points C, E, and D and is perpendicular to line AB at point E. Line FG intersects these two lines at the point E and passes through points F, E, and G. The angle BEF is labeled 120 degrees.

Answer 1

To find the measure of angle AEF, we can use the fact that lines AB and CD are perpendicular at point E. Since line AB is horizontal and line CD is vertical, we know that angle AEF and angle BEF are angles that together form a straight line at point E.

The angles AEF and BEF are supplementary since they are on the same line along line AB.

Given that angle BEF is 120 degrees, we can calculate angle AEF as follows:

$$\text{Angle AEF}+\text{Angle BEF}={180}^{\circ }$$

Substituting the value of angle BEF:

$$\text{Angle AEF}+{120}^{\circ }={180}^{\circ }$$

Now, solving for angle AEF:

$$\text{Angle AEF}={180}^{\circ }-{120}^{\circ }={60}^{\circ }$$

Thus, the measure of angle AEF is $\boxed{{\displaystyle 60}}$.