https://file.aiquickdraw.com/mathbot/file/1729792791544wonwxkv6.jpg

Let's analyze the image to solve the problem. The quadrilateral given in the image is \( KJML \), and we are asked to find the measures of its interior angles. Each angle is represented as an expression involving the variable \( x \). 

### Step 1: Interior angle sum of a quadrilateral
For any quadrilateral, the sum of the interior angles is always \( 360^\circ \). Hence, we can write the equation:

\[
m\angle J + m\angle K + m\angle L + m\angle M = 360^\circ
\]

### Step 2: Express each angle in terms of \( x \)
From the diagram, the angle expressions are:
- \( m\angle J = 3x - 6^\circ \)
- \( m\angle K = x + 10^\circ \)
- \( m\angle L = x^\circ \)
- \( m\angle M = 2x - 8^\circ \)

### Step 3: Set up the equation
Now, substitute the expressions for each angle into the equation for the sum of the interior angles:

\[
(3x - 6) + (x + 10) + x + (2x - 8) = 360
\]

### Step 4: Simplify the equation
First, combine the like terms:

\[
3x + x + x + 2x - 6 + 10 - 8 = 360
\]
\[
7x - 4 = 360
\]

### Step 5: Solve for \( x \)
Now, solve for \( x \):

\[
7x = 360 + 4
\]
\[
7x = 364
\]
\[
x = \frac{364}{7}
\]
\[
x = 52
\]

### Step 6: Calculate the measure of each angle
Substitute \( x = 52 \) back into the expressions for each angle:
- \( m\angle J = 3(52) - 6 = 156 - 6 = 150^\circ \)
- \( m\angle K = 52 + 10 = 62^\circ \)
- \( m\angle L = 52^\circ \)
- \( m\angle M = 2(52) - 8 = 104 - 8 = 96^\circ \)

### Final Answer:
- \( m\angle J = 150^\circ \)
- \( m\angle K = 62^\circ \)
- \( m\angle L = 52^\circ \)
- \( m\angle M = 96^\circ \)

Would you like further details on any part of this solution? 

Here are 5 related questions for practice:
1. How do you calculate the sum of interior angles for a polygon with \( n \) sides?
2. If one of the angles of a quadrilateral is a right angle, how does this affect the remaining angles?
3. How would the solution change if this was a cyclic quadrilateral?
4. What if the angles were expressed in radians instead of degrees?
5. How can you confirm that the sum of the calculated angles is correct?

**Tip**: Always verify that the sum of your calculated angles matches the expected sum for the polygon!

Find the measure of each interior angle in quadrilateral KJML with angle expressions: m∠J = (3x - 6)°, m∠K = (x + 10)°, m∠L = x°, m∠M = (2x - 8)°.

Learn how to solve for the interior angles of quadrilateral KJML by setting up and solving an algebraic equation. The problem covers geometry and algebra, using the sum of the interior angles of a quadrilateral and basic angle expressions. Ideal for students in Grades 8-10.

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