https://file.aiquickdraw.com/mathbot/file/17302171233260f4dv2qd.jpg

Ashley draws two angles shown.
 


If angles JKL and LKM are complementary, what is the value of x?
A.8
B.22
C.9
D.68

To solve for \( x \) in this problem, let's break down the information provided:

1. **Given Angles**: 
   - Angle \( JKL = (6x + 14)^\circ \)
   - Angle \( LKM = 22^\circ \)
   
2. **Complementary Angles**: Angles \( JKL \) and \( LKM \) are complementary, meaning their measures add up to \( 90^\circ \).

So, we can set up the equation:
\[
(6x + 14) + 22 = 90
\]

3. **Solve for \( x \)**:
   - Simplify the equation:
     \[
     6x + 14 + 22 = 90
     \]
   - Combine like terms:
     \[
     6x + 36 = 90
     \]
   - Subtract 36 from both sides:
     \[
     6x = 54
     \]
   - Divide by 6:
     \[
     x = 9
     \]

So, the value of \( x \) is **9**, which corresponds to **Option C**.

---

Would you like a further breakdown of each step or have additional questions?

Here are 5 related questions to extend your understanding:

1. What are supplementary angles, and how do they differ from complementary angles?
2. If angle \( JKL \) was increased by 5 degrees, how would that affect the value of \( x \)?
3. How would the solution change if angle \( LKM \) was 25 degrees instead of 22 degrees?
4. What is the measure of angle \( JKL \) when \( x = 9 \)?
5. How can we check that two angles are complementary?

**Tip:** Remember that complementary angles always add up to 90 degrees, which is useful when working with right-angle problems.

Ashley draws two angles shown. If angles JKL and LKM are complementary, what is the value of x? A.8 B.22 C.9 D.68

Learn how to solve a problem involving complementary angles by finding the value of x when angle JKL is (6x + 14)° and angle LKM is 22°. Suitable for students in Grades 7-8.

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