If the vertex angle of an isosceles triangle measures 57°, what are the measures of the base angles?

Explanation

Given: Vertex angle \( \angle V = 57^\circ \). Let each base angle be \( x \).

Sum of angles in a triangle: \[ \angle V + \angle B_1 + \angle B_2 = 180^\circ \]

Substitute the known values: \[ 57^\circ + x + x = 180^\circ \]

Simplify: \[ 57^\circ + 2x = 180^\circ \]

Subtract 57° from both sides: \[ 2x = 180^\circ - 57^\circ = 123^\circ \]

Divide by 2: \[ x = \frac{123^\circ}{2} = 61.5^\circ \]

Answer: Each base angle measures \( 61.5^\circ \).