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°.