Question

what is the measure of ∠a?

Explanation:

Step1: Determine the type of triangle

Since \(AB = AC\), \(\triangle ABC\) is an isosceles triangle. So, \(\angle B=\angle C = 46^{\circ}\).

Step2: Use the triangle - angle sum formula

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle A=x\). Then \(x+\angle B+\angle C = 180^{\circ}\). Substitute \(\angle B = \angle C=46^{\circ}\) into the formula: \(x + 46^{\circ}+46^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(46^{\circ} + 46^{\circ})\)
\(x=180^{\circ}-92^{\circ}\)
\(x = 88^{\circ}\)

Answer:

\(88\)