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Let's analyze the problem.

We are given two angles that form a linear pair, which means their sum is \(180^\circ\). The angles are congruent, so they are equal in measure. One angle is given as \(5x + 45^\circ\), and the other is given as \(\frac{45y}{2}\). We need to find the values of \(x\) and \(y\).

### Step 1: Equation for the linear pair
Since the two angles form a linear pair, their sum is:

\[
(5x + 45) + \frac{45y}{2} = 180
\]

### Step 2: Set up an equation for congruent angles
Because the angles are congruent, we can also set them equal to each other:

\[
5x + 45 = \frac{45y}{2}
\]

Now, we can solve this system of equations to find \(x\) and \(y\).

Let me solve this step by step.The solution to the system of equations is:

- \( x = 9^\circ \)
- \( y = 4^\circ \)

So, the values of \(x\) and \(y\) are 9 and 4, respectively.

Do you need further details or have any questions?

Here are 5 related questions to further your understanding:

1. What is the concept of a linear pair of angles?
2. Why must the sum of a linear pair of angles equal \(180^\circ\)?
3. How do we know that the angles are congruent in this problem?
4. Can two congruent angles always form a linear pair?
5. What happens if the two angles in the linear pair are not congruent?

**Tip:** When dealing with systems of equations, always try to simplify them as much as possible before solving!

Two lines intersect to form a linear pair of congruent angles. The measure of one angle is (5x + 45)° and the measure of the other angle is (45y / 2)°. Find the values of x and y.

Learn how to solve for x and y in a problem involving a linear pair of congruent angles. This step-by-step solution covers key algebraic concepts and geometry theorems, including the Linear Pair Theorem and the concept of congruent angles. Ideal for students in Grades 8-10.

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