Question

enter the given angle measure into the diagram.
given:

• ∠mez ≅ ∠ber.
• m∠mez = 20°.

enter each measure required to calculate m∠meb, starting
with the given information.
the measure of ∠meb can be calculated.
the measure of ∠meb can not be calculated.
diagram notes:

Explanation:

Step1: Use the property of vertical angles

Since \(\angle MEZ\cong\angle BER\) (vertical angles are congruent), and \(m\angle MEZ = 20^{\circ}\), then \(m\angle BER=20^{\circ}\).

Step2: Use the property of a straight - angle

We know that \(\angle MEZ+\angle MEB+\angle BER = 180^{\circ}\) (a straight - angle measures \(180^{\circ}\)). Substitute \(m\angle MEZ = 20^{\circ}\) and \(m\angle BER = 20^{\circ}\) into the equation: \(20^{\circ}+m\angle MEB + 20^{\circ}=180^{\circ}\).

Step3: Solve for \(m\angle MEB\)

Simplify the left - hand side of the equation: \(m\angle MEB+40^{\circ}=180^{\circ}\). Then, using the subtraction property of equality, \(m\angle MEB=180^{\circ}- 40^{\circ}=140^{\circ}\).

Answer:

\(m\angle MEB = 140^{\circ}\)