In ΔJKL, m, angle, J, equals, left parenthesis, 8, x, minus, 8, right parenthesis, degreesm∠J=(8x−8) 
∘
 , m, angle, K, equals, left parenthesis, 2, x, minus, 8, right parenthesis, degreesm∠K=(2x−8) 
∘
 , and m, angle, L, equals, left parenthesis, 5, x, minus, 14, right parenthesis, degreesm∠L=(5x−14) 
∘
 . What is the value of x, question markx?

In a triangle, the sum of the measures of the three angles is always \( 180^\circ \). Therefore, for \(\triangle JKL\):

\[
m\angle J + m\angle K + m\angle L = 180^\circ
\]

### Step 1: Substitute the expressions for the angles.
\[
(8x - 8) + (2x - 8) + (5x - 14) = 180
\]

### Step 2: Simplify the equation by combining like terms.
\[
8x + 2x + 5x - 8 - 8 - 14 = 180
\]
\[
15x - 30 = 180
\]

### Step 3: Solve for \(x\).
Add 30 to both sides:
\[
15x = 210
\]

Divide both sides by 15:
\[
x = 14
\]

### Final Answer:
\[
x = 14
\]

### Verification:
Substitute \(x = 14\) into the expressions for the angles:
- \(m\angle J = 8x - 8 = 8(14) - 8 = 112 - 8 = 104^\circ\),
- \(m\angle K = 2x - 8 = 2(14) - 8 = 28 - 8 = 20^\circ\),
- \(m\angle L = 5x - 14 = 5(14) - 14 = 70 - 14 = 56^\circ\).

Check the sum:
\[
104^\circ + 20^\circ + 56^\circ = 180^\circ
\]

The calculation is correct.

---

Would you like further details or clarification?  

### Related Questions:
1. What is the relationship between the interior angles of a triangle?
2. How do you find the value of an angle in a triangle when two are given?
3. What are the different types of triangles based on their angles?
4. Can the angles of a triangle ever be negative?
5. How does the triangle angle sum property extend to polygons?

### Tip:
Always double-check your work by substituting back into the original equations to verify the solution!

In ΔJKL, m∠J = (8x - 8)°, m∠K = (2x - 8)°, and m∠L = (5x - 14)°. What is the value of x?

Learn how to solve for x in a triangle when given angle expressions. This problem involves the Triangle Angle Sum Theorem, simplifying algebraic expressions, and solving for a variable. Suitable for students in Grades 7-9.

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