Question

find the values of x and y given that abcd ≅ efgh. (4y - 4)° (10x + 65)° b c 135° a d h g 28° x = □ and y = □

Explanation:

Step1: Use the property of congruent polygons

Since \(ABCD\cong EFGH\), corresponding angles are equal. So, \(\angle A=\angle E\) and \(\angle B=\angle F\).
Given \(\angle A = 28^{\circ}\), \(\angle E=(4y - 4)^{\circ}\), then \(4y-4=28\).
Given \(\angle B = 135^{\circ}\), \(\angle F=(10x + 65)^{\circ}\), then \(10x+65 = 135\).

Step2: Solve for \(x\)

For \(10x+65 = 135\), subtract \(65\) from both sides:
\(10x=135 - 65\)
\(10x=70\)
Divide both sides by \(10\): \(x = 7\)

Step3: Solve for \(y\)

For \(4y-4=28\), add \(4\) to both sides:
\(4y=28 + 4\)
\(4y=32\)
Divide both sides by \(4\): \(y = 8\)

Answer:

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