Question

find the measure of \\( \angle bac \\).
\\( m \angle bac = \\)
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Explanation:

Step1: Identify the triangle type

The triangle is equilateral (all sides equal), so it's also equiangular. But wait, no, actually, since two sides are marked equal (the sides adjacent to \( \angle BAC \) and \( \angle BCA \)), it's an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \( \angle BAC=\angle BCA = x\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(x + x+80^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 80^{\circ}\).
\(2x = 100^{\circ}\).
Divide both sides by 2: \(x=\frac{100^{\circ}}{2}\).

Answer:

\(50^{\circ}\)