Question

find the values of x and y given that abcd ≅ efgh.

x = □ and y = □

Explanation:

Step1: Use the property of congruent polygons

Since \(ABCD\cong EFGH\), corresponding angles are equal. \(\angle A=\angle E\) and \(\angle B=\angle F\).
We know that \(\angle A = 28^{\circ}\), so \(4y-4=28\).

Step2: Solve for \(y\)

For the equation \(4y - 4=28\), add \(4\) to both sides:
\(4y-4 + 4=28 + 4\), which simplifies to \(4y=32\).
Divide both sides by \(4\): \(y=\frac{32}{4}=8\).

Step3: Solve for \(x\)

We know that \(\angle B = 135^{\circ}\), so \(10x+65 = 135\).
Subtract \(65\) from both sides: \(10x+65-65=135 - 65\), which gives \(10x=70\).
Divide both sides by \(10\): \(x=\frac{70}{10}=7\).

Answer:

\(x = 7\) and \(y = 8\)