Question

enter the given angle measure into the diagram.
given:

• ∠ceq ≅ ∠bed
• m∠bed = 110°

enter each measure required to calculate m∠beq, starting with the given information.

• the measure of ∠beq can be calculated.

m∠beq =

• the measure of ∠beq can not be calculated.

diagram notes:

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle BED\) and \(\angle BEQ\) are supplementary (they form a linear - pair), and \(\angle CEQ\cong\angle BED = 110^{\circ}\).
The sum of angles in a linear - pair is \(180^{\circ}\). Let \(m\angle BEQ=x\).
We know that \(m\angle BED + m\angle BEQ=180^{\circ}\) (by the definition of a linear - pair of angles).

Step2: Solve for \(m\angle BEQ\)

Substitute \(m\angle BED = 110^{\circ}\) into the equation \(m\angle BED + m\angle BEQ = 180^{\circ}\).
We get \(110^{\circ}+x = 180^{\circ}\).
Subtract \(110^{\circ}\) from both sides of the equation: \(x=180^{\circ}-110^{\circ}\).

Answer:

\(m\angle BEQ = 70^{\circ}\)