Question

1. a figure is shown below. what is the ( mangle ceb )?
2. in the given triangle, ( ab = ac ) and

Explanation:

Step1: Use the property of linear pair

Since \(\angle CEB\) and \(\angle BED\) form a linear - pair (they are adjacent angles and their non - common sides form a straight line), we know that \(\angle CEB+\angle BED = 180^{\circ}\). Given \(\angle CEB=(4x - 22)^{\circ}\) and \(\angle BED=(2x + 4)^{\circ}\), we have the equation \((4x-22)+(2x + 4)=180\).

Step2: Simplify the equation

Combine like terms: \(4x+2x-22 + 4=180\), which simplifies to \(6x-18 = 180\).
Add \(18\) to both sides of the equation: \(6x-18+18=180 + 18\), so \(6x=198\).
Divide both sides by \(6\): \(x=\frac{198}{6}=33\).

Step3: Find the measure of \(\angle CEB\)

Substitute \(x = 33\) into the expression for \(\angle CEB\).
\(\angle CEB=(4x-22)^{\circ}\), so \(\angle CEB=4\times33-22\).
First, calculate \(4\times33 = 132\), then \(132-22=110\).

Answer:

\(110^{\circ}\)