Question

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

Explanation:

Step1: Sum angles of triangle to 180°

$\angle S + \angle T + \angle U = 180^\circ$

Step2: Substitute given angle expressions

$(5x+9) + (3x+8) + (x-8) = 180$

Step3: Simplify left-hand side

$5x+3x+x+9+8-8 = 180$
$9x + 9 = 180$

Step4: Solve for $x$

$9x = 180 - 9$
$9x = 171$
$x = \frac{171}{9} = 19$

Step5: Calculate $m\angle S$

$m\angle S = 5x + 9 = 5(19) + 9$

Answer:

$104^\circ$