m<JKL and m<MNP are supplementary; m<JKL = 3x -5 and m<MNP = 23x+3. Make a sketch what re m<JKL and<MNP? write an equation and solve

Let's break this down step by step:

### Problem Information:
- \( m \angle JKL \) and \( m \angle MNP \) are supplementary, which means their measures add up to 180 degrees.
- The measure of \( \angle JKL \) is given as \( 3x - 5 \).
- The measure of \( \angle MNP \) is given as \( 23x + 3 \).

### Step 1: Set Up the Equation
Since \( m \angle JKL \) and \( m \angle MNP \) are supplementary, we can write the following equation:

\[
(3x - 5) + (23x + 3) = 180
\]

### Step 2: Solve the Equation
1. Combine like terms:

\[
3x + 23x - 5 + 3 = 180
\]

\[
26x - 2 = 180
\]

2. Add 2 to both sides:

\[
26x = 182
\]

3. Solve for \( x \):

\[
x = \frac{182}{26} = 7
\]

### Step 3: Find the Measures of \( \angle JKL \) and \( \angle MNP \)
Now substitute \( x = 7 \) back into the expressions for the angle measures:

- \( m \angle JKL = 3x - 5 = 3(7) - 5 = 21 - 5 = 16^\circ \)
- \( m \angle MNP = 23x + 3 = 23(7) + 3 = 161 + 3 = 164^\circ \)

### Step 4: Verify the Solution
Check if the angles are supplementary:

\[
16^\circ + 164^\circ = 180^\circ
\]

So, the solution is correct.

### Sketch Explanation
- The two angles \( \angle JKL \) and \( \angle MNP \) are supplementary, meaning they form a straight line when placed next to each other. You can imagine two adjacent angles sharing a common ray, forming a line with the sum of 180 degrees.

Would you like me to generate a sketch of the two angles?

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Here are five related questions:
1. What does it mean for two angles to be supplementary?
2. Can angles be supplementary if both are obtuse?
3. How do you solve for \( x \) when angles are complementary instead of supplementary?
4. Can two angles still be supplementary if they are not adjacent?
5. What would happen if one angle's measure was negative?

**Tip:** Always double-check if your equation correctly represents the relationship between the given angles before solving.

m<JKL and m<MNP are supplementary; m<JKL = 3x - 5 and m<MNP = 23x+3. Make a sketch what are m<JKL and m<MNP? Write an equation and solve.

Learn how to solve the problem of supplementary angles with measures m<JKL = 3x - 5 and m<MNP = 23x + 3. This solution involves setting up and solving a linear equation to find the values of x and the angle measures. Suitable for students in Grades 7-9.

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