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.

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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!