https://file.aiquickdraw.com/mathbot/file/1729834165139h7arfz77.jpg

We are given the following information from the image:

- \( m \angle JKL = 112^\circ \)
- \( m \angle JKC = 7x - 3 \)
- \( m \angle CKL = 6x - 2 \)

To solve for \( m \angle CKL \), let's begin by noting that \( \angle JKC + \angle CKL = \angle JKL \), because \( \angle JKC \) and \( \angle CKL \) are adjacent angles that form the larger angle \( \angle JKL \).

### Step 1: Set up the equation

We can write the equation as:
\[
(7x - 3) + (6x - 2) = 112^\circ
\]

### Step 2: Solve for \( x \)

Simplify the equation:
\[
7x - 3 + 6x - 2 = 112
\]
\[
13x - 5 = 112
\]
Now, add 5 to both sides:
\[
13x = 117
\]
Solve for \( x \):
\[
x = \frac{117}{13} = 9
\]

### Step 3: Find \( m \angle CKL \)

Substitute \( x = 9 \) into the expression for \( m \angle CKL \):
\[
m \angle CKL = 6x - 2 = 6(9) - 2 = 54 - 2 = 52^\circ
\]

Thus, \( m \angle CKL = 52^\circ \).

Would you like further details or have any questions? 

Here are 5 related questions for further practice:
1. What is the measure of \( m \angle JKC \) when \( x = 9 \)?
2. If \( m \angle JKC = 7x - 3 \), what is the relationship between \( x \) and \( m \angle CKL \)?
3. How do adjacent angles relate to the larger angle they form?
4. Can you solve for \( x \) if the measure of angle \( JKL \) was different, say \( 100^\circ \)?
5. What would happen to the angles if \( JKC \) and \( CKL \) were supplementary?

**Tip:** When solving for unknowns in adjacent angle problems, always set up an equation based on their sum forming a known larger angle.

m∠JKL = 112°, m∠JKC = 7x - 3, and m∠CKL = 6x - 2. Find m∠CKL.

Learn how to solve for m∠CKL using the given angle relationships: m∠JKL = 112°, m∠JKC = 7x - 3, and m∠CKL = 6x - 2. A step-by-step solution covers key concepts of algebra and geometry, suitable for students in Grades 8-10.

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