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 a straight - line angle

A straight - line angle measures \(180^{\circ}\). The sum of \(\angle CEQ\) and \(\angle BEQ\) and \(\angle BED\) forms a straight - line at point \(E\). But we know \(\angle CEQ\cong\angle BED\), and \(m\angle BED = 110^{\circ}\). Let \(x=m\angle BEQ\). Then \(m\angle CEQ + m\angle BEQ+m\angle BED=360^{\circ}\) (full - circle angle is \(360^{\circ}\)), or using the fact that \(\angle CEQ\) and \(\angle BED\) are congruent and considering the non - overlapping angles around point \(E\). Another way: Since \(\angle CEQ\cong\angle BED\) and \(m\angle BED = 110^{\circ}\), and \(\angle CEQ+\angle BEQ+\angle BED = 360^{\circ}\) (angles around a point). Substitute \(m\angle CEQ = 110^{\circ}\) and \(m\angle BED=110^{\circ}\) into the equation \(110^{\circ}+x + 110^{\circ}=360^{\circ}\).

Step2: Solve for \(x\)

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Answer:

\(140\)