Question

1. what is the vertex angle of an isosceles triangle if the base angle is 88 degrees? a) 4 b) 180 c) 60 d) 45

Explanation:

Step1: Recall the property of isosceles triangle

In an isosceles triangle, the base angles are equal. Let the base angles be \( \angle B=\angle C = 88^{\circ}\)

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 \( \angle B = \angle C=88^{\circ}\) into the equation: \( \angle A+88^{\circ}+88^{\circ}=180^{\circ}\)
\( \angle A=180^{\circ}-(88^{\circ} + 88^{\circ})\)
\( \angle A=180^{\circ}-176^{\circ}\)
\( \angle A = 4^{\circ}\)

Answer:

\(4\)