Question

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in the diagram, polygon ( a b c d cong ) polygon ( p q r s ).
find the value of ( x )

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, \(2x + 4=80\).

Step2: Solve the equation for \(x\)

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

Answer:

\(38\)