the base angle of an isosceles triangle measures 54°. what is the measure of its vertex angle?\n27°\n36°\n54°…

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Identify base - angle property of isosceles triangle

In an isosceles triangle, the two base angles are equal. Let the base angle be (b = 54^{\circ}), and the vertex angle be (v).

Step3: Set up the equation

We know that (b + b+v=180^{\circ}), substituting (b = 54^{\circ}) into the equation, we get (54^{\circ}+54^{\circ}+v = 180^{\circ}).

Step4: Solve for the vertex angle

First, simplify the left - hand side: (108^{\circ}+v=180^{\circ}). Then, subtract (108^{\circ}) from both sides: (v=180^{\circ}- 108^{\circ}=72^{\circ}).

Answer:

(72^{\circ})