Question

find the value of x.
in the diagram, polygon abcd ≅ polygon pqrs.

Explanation:

Step1: Use the property of congruent polygons

Since polygon \(ABCD\cong\) polygon \(PQRS\), their corresponding angles are equal. Angle \(A\) in polygon \(ABCD\) corresponds to angle \(R\) in polygon \(PQRS\). So, we set up the equation \(2x + 4=80\).

Step2: Solve the equation for \(x\)

Subtract \(4\) from both sides of the equation: \(2x+4 - 4=80 - 4\), which simplifies to \(2x = 76\). Then divide both sides by \(2\): \(x=\frac{76}{2}\).

Answer:

\(x = 38\)