Question

the base angle of an isosceles triangle measures 54°. what is the measure of its vertex angle? 27° 36° 54° 72°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Identify base - angles in isosceles triangle

In an isosceles triangle, the two base - angles are equal. Given one base - angle is 54°, so the sum of the two base - angles is 54°+54° = 108°.

Step3: Calculate the vertex angle

Let the vertex angle be \(x\). Then \(x+108^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-108^{\circ}=72^{\circ}\).

Answer:

D. 72°