Question

What is the measure of angle DEB in degrees? Explain howyou know. i need help

Answer 1

The measure of angle DEB is 50 degrees.

In the image, lines AB and CD intersect at point E. Angle DEB is a vertical angle to angle AEB, which is labeled as 50 degrees. Vertical angles are always equal in measure, so angle DEB must also measure 50 degrees.

Another way to think about this problem is to use the following theorem:

Angle Addition Theorem: The sum of the measures of the angles in a triangle is 180 degrees.

We can use this theorem to find the measure of angle DEB by first finding the measure of angle AED.

Angle AED + Angle DEB = Angle AEB

Angle AED + 50 degrees = 50 degrees

Angle AED = 0 degrees

Since angle AED is 0 degrees, then angle DEB must be 50 degrees.

Answer 2

Looking at the given diagram, angle AEC and angle DEB share the same vertex, E. They are described as vertically opposit angles. In geometry, vertically opposite angles are equal. This means that

Angle DEB = angl AEC = 50 degrees