Question

1. what is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°? 69° 96° 138° 84°

Explanation:

Step1: Recall the properties of isosceles triangle

In an isosceles triangle, the base angles are equal. Let the base angles be \( \angle B=\angle C = 42^{\circ}\)

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the vertex angle be \( \angle A\). Then \( \angle A+\angle B+\angle C=180^{\circ}\)
Substitute \( \angle B = \angle C=42^{\circ}\) into the formula: \( \angle A+42^{\circ}+42^{\circ}=180^{\circ}\)

Step3: Solve for the vertex angle

\( \angle A=180^{\circ}-(42^{\circ} + 42^{\circ})\)
\( \angle A=180^{\circ}-84^{\circ}\)
\( \angle A = 96^{\circ}\)

Answer:

\(96^{\circ}\) (the second option)