Question

in δjkl, m∠j = (4x − 1)°, m∠k = (7x − 18)°, and m∠l = (x − 5)°. what is the value of x?

Explanation:

Step1: Recall triangle angle sum property

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: Combine like terms

First, combine the \(x\) terms: \(4x+7x+x = 12x\).
Then, combine the constant terms: \(-1-18 - 5=-24\).
So the equation becomes \(12x-24 = 180\).

Step3: Solve for \(x\)

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

Answer:

\(17\)