Question

for the following intersection, the measurements of the indicated angles are represented by the expressions $mangle s=(6x + 78)^{circ}$ and $mangle t=(6x + 174)^{circ}$. what are the numerical angle measurements of $angle s$ and $angle t$?

Explanation:

Step1: Identify angle relationship

Angles $\angle s$ and $\angle t$ are supplementary, so $m\angle s + m\angle t=180^{\circ}$.
$$(6x + 78)+(6x + 174)=180$$

Step2: Simplify the equation

Combine like - terms:
$$12x+252 = 180$$

Step3: Solve for $x$

Subtract 252 from both sides:
$$12x=180 - 252$$
$$12x=- 72$$
Divide both sides by 12:
$$x=-6$$

Step4: Find $m\angle s$

Substitute $x = - 6$ into the expression for $m\angle s$:
$$m\angle s=6x + 78=6\times(-6)+78=-36 + 78 = 42^{\circ}$$

Step5: Find $m\angle t$

Substitute $x = - 6$ into the expression for $m\angle t$:
$$m\angle t=6x + 174=6\times(-6)+174=-36+174 = 138^{\circ}$$

Answer:

$m\angle s = 42^{\circ}$
$m\angle t = 138^{\circ}$