Question

in $\triangle stu$, $mangle s=(5x + 4)^{circ}$, $mangle t=(4x - 18)^{circ}$, and $mangle u=(2x + 7)^{circ}$. what is the value of $x$?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle S+m\angle T + m\angle U=180^{\circ}\).
Substitute the given angle - measures: \((5x + 4)+(4x-18)+(2x + 7)=180\).

Step2: Combine like - terms

First, combine the \(x\) terms: \(5x+4x + 2x=11x\), and combine the constant terms: \(4-18 + 7=-7\).
The equation becomes \(11x-7 = 180\).

Step3: Isolate the variable \(x\)

Add 7 to both sides of the equation: \(11x-7+7=180 + 7\), which simplifies to \(11x=187\).
Then divide both sides by 11: \(x=\frac{187}{11}\).

Step4: Calculate the value of \(x\)

\(x = 17\).

Answer:

\(17\)