Question

question
in $\triangle jkl$, $m\angle j = (4x - 1)\degree$, $m\angle k = (7x - 18)\degree$, and $m\angle l = (x - 5)\degree$. 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 measures: \((4x - 1)+(7x - 18)+(x - 5)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms:

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Add \(24\) to both sides of the equation: \(12x-24 + 24=180+24\), which gives \(12x=204\).
Divide both sides by \(12\): \(x=\frac{204}{12}=17\).

Answer:

\(x = 17\)