Question

in $\triangle stu$, $m\angle s=(5x + 9)^{circ}$, $m\angle t=(3x + 8)^{circ}$, and $m\angle u=(x - 8)^{circ}$. find $m\angle s$.

Explanation:

Step1: Sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^\circ\). So, \(m\angle S + m\angle T + m\angle U = 180^\circ\).
Substitute the given angle expressions: \((5x + 9) + (3x + 8) + (x - 8) = 180\).

Step2: Simplify the equation

Combine like terms: \(5x + 3x + x + 9 + 8 - 8 = 180\)
Simplify: \(9x + 9 = 180\).

Step3: Solve for \(x\)

Subtract 9 from both sides: \(9x = 180 - 9 = 171\)
Divide by 9: \(x = \frac{171}{9} = 19\).

Step4: Find \(m\angle S\)

Substitute \(x = 19\) into \(m\angle S = (5x + 9)^\circ\):
\(m\angle S = 5(19) + 9 = 95 + 9 = 104\).

Answer:

\(104^\circ\)