Question

what is the measure of each of the two base angles?
base angles measure: type your answer...

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Identify the triangle type

The triangle is isosceles (since it's above a rectangle, the two base sides are equal), so the two base angles are equal. Let each base angle be \(x\).

Step3: Set up the equation

\(80^\circ + x + x = 180^\circ\)

Step4: Solve for \(x\)

Simplify: \(80^\circ + 2x = 180^\circ\)
Subtract \(80^\circ\): \(2x = 180^\circ - 80^\circ = 100^\circ\)
Divide by 2: \(x = \frac{100^\circ}{2} = 50^\circ\)

Answer:

\(50^\circ\)