Question

in exercises 7 and 8, find the values of x and y. (see example 2.)

1. abcd ≅ efgh
2. △mnp ≅ △tus

Explanation:

Step1: Use the property of congruent polygons (corresponding angles are equal)

Since \(ABCD\cong EFGH\), then \(\angle A=\angle E\) and \(\angle B = \angle F\).
We know that \(\angle A = 28^{\circ}\), so \(4y-4=28\).
Solve the equation \(4y - 4=28\):
Add \(4\) to both sides: \(4y=28 + 4=32\).
Divide both sides by \(4\): \(y=\frac{32}{4}=8\).

Step2: Also, since \(ABCD\cong EFGH\), \(\angle B=135^{\circ}\), and \(\angle B=\angle F\), so \(10x + 65=135\).

Solve the equation \(10x+65 = 135\):
Subtract \(65\) from both sides: \(10x=135 - 65 = 70\).
Divide both sides by \(10\): \(x=\frac{70}{10}=7\).

Answer:

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