https://file.aiquickdraw.com/mathbot/file/1726961712572uel1qq8t.jpg

The problem in the image describes two lines that form a linear pair of angles, meaning the sum of the angles is 180°. One angle is expressed as \( 2x^\circ \), and the other is expressed as \( (9y - 9)^\circ \). We're asked to find the values of \( x \) and \( y \).

The two angles form a linear pair, so their sum must be:

\[
2x + (9y - 9) = 180
\]

We are also given that \( x^\circ = 45^\circ \) and \( y^\circ = 11^\circ \). Let's substitute these values into the equation.

1. Substituting \( x = 45 \) into \( 2x \):

\[
2(45) = 90^\circ
\]

2. Substituting \( y = 11 \) into \( (9y - 9) \):

\[
9(11) - 9 = 99 - 9 = 90^\circ
\]

Now we verify:

\[
90^\circ + 90^\circ = 180^\circ
\]

So, both angles indeed add up to 180°, meaning the solution is correct. Therefore:

- \( x = 45^\circ \)
- \( y = 11^\circ \)

Would you like more details or explanations? 

Here are some related questions to consider:
1. What is a linear pair of angles in geometry?
2. How do you solve for two unknowns in an equation involving angles?
3. Why do angles in a linear pair always sum to 180°?
4. Can a linear pair of angles be unequal? Why or why not?
5. How can this type of problem be extended to angles not forming a linear pair?

**Tip:** In problems involving linear pairs, always check if the sum of the angles equals 180°.

Two lines intersect to form a linear pair with equal measures. One angle has the measure 2x°, and the other angle has the measure (9y - 9)°. Find the values of x and y.

Learn how to solve for x and y in a linear pair of angles problem, where one angle is expressed as 2x° and the other as (9y - 9)°. This problem demonstrates key algebraic concepts and the linear pair theorem, suitable for students in Grades 7-10.

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