Question

lines ce and ad intersect at b. what is the measure of angle dbe? what is the measure of angle cbd? what is the measure of angle abe? name an angle congruent to angle abe? 33 degrees 123 degrees 57 degrees 133 degrees 180 degrees 90 degrees angle cbd angle abc angle dbe

Explanation:

Step1: Identify vertical - angles

Vertical angles are congruent. Angle ABE and angle CBD are vertical angles, and angle ABC and angle DBE are vertical angles.

Step2: Find measure of angle ABE

Given an angle of 57 degrees. Angle ABE and the 57 - degree angle are vertical angles. So, $\angle ABE = 57^{\circ}$.

Step3: Find measure of angle CBD

Since angle ABE and angle CBD are vertical angles, $\angle CBD=\angle ABE = 57^{\circ}$.

Step4: Find measure of angle DBE

Angle DBE and the 57 - degree angle are supplementary (they form a straight - line, and the sum of angles on a straight - line is 180 degrees). So, $\angle DBE=180 - 57=123^{\circ}$.

Answer:

Name an angle congruent to angle ABE: angle CBD
What is the measure of angle ABE? 57 degrees
What is the measure of angle CBD? 57 degrees
What is the measure of angle DBE? 123 degrees