Question

what is the value of b?

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Explanation:

Step1: Recall the property of isosceles triangle

In \(\triangle CED\), since \(CE = CD\) (marked by the same tick - marks), \(\triangle CED\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle E=\angle D = b\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle CED\), we have \(\angle C+\angle E+\angle D = 180^{\circ}\). Substituting \(\angle C = 88^{\circ}\) and \(\angle E=\angle D = b\) into the equation, we get \(88^{\circ}+b + b=180^{\circ}\).

Step3: Solve the equation for \(b\)

Combine like terms: \(88^{\circ}+2b=180^{\circ}\). Subtract \(88^{\circ}\) from both sides: \(2b=180^{\circ}- 88^{\circ}=92^{\circ}\). Divide both sides by 2: \(b=\frac{92^{\circ}}{2}=46^{\circ}\).

Answer:

\(46\)