Question

△abc is an isosceles triangle, where \\( \overline { a b } \cong \overline { a c } \\).
the measure of \\( \angle a \\) is \\( 116 ^ { \circ } \\). what are the measures of the missing angles?
\\( m \angle b \\)
\\( m \angle b = \\)
\\( m \angle c \\)
\\( m \angle c = \\)

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). Let \(m\angle B = m\angle C=x\) (since \(AB\cong AC\), base - angles are equal). Then \(x + x+116^{\circ}=180^{\circ}\).

Step2: Solve the equation

Combine like terms: \(2x+116^{\circ}=180^{\circ}\). Subtract \(116^{\circ}\) from both sides: \(2x=180^{\circ}- 116^{\circ}=64^{\circ}\). Divide by 2: \(x = 32^{\circ}\).

Answer:

\(m\angle B = 32^{\circ}\)
\(m\angle C = 32^{\circ}\)