Question

in \\( \triangle jkl, m \angle j=(8 x-8)^{\circ}, m \angle k=(2 x-8)^{\circ} \\), and \\( m \angle l=(5 x-14)^{\circ} \\). what is the value of \\( x \\)?

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle J+m\angle K + m\angle L=180^{\circ}\).
Substitute the given angle expressions: \((8x - 8)+(2x - 8)+(5x - 14)=180\).

Step2: Combine like terms

First, combine the \(x\) - terms: \(8x+2x + 5x=15x\).
Then, combine the constant terms: \(-8-8 - 14=-30\).
The equation becomes \(15x-30 = 180\).

Step3: Solve for \(x\)

Add \(30\) to both sides of the equation: \(15x-30 + 30=180+30\), which simplifies to \(15x=210\).
Divide both sides by \(15\): \(x=\frac{210}{15}\).

Answer:

\(x = 14\)