Question

the measure of the vertex angle of an isosceles triangle is 64°. what is the measure of one of the triangles base angles? enter deg after any value that is in degrees. check answer

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Let the measure of each base angle be \(x\)

Since the triangle is isosceles, the two base angles are equal. The vertex angle is \(64^{\circ}\). So, \(x + x+64^{\circ}=180^{\circ}\).

Step3: Simplify the equation

\(2x=180^{\circ}- 64^{\circ}\).
\(2x = 116^{\circ}\).

Step4: Solve for \(x\)

\(x=\frac{116^{\circ}}{2}\).
\(x = 58^{\circ}\).

Answer:

\(58\) deg