Question

problem 6: ∠stu measures 7 more than twice its complement. what is the supplement of ∠stu?

Explanation:

Step1: Define the angle and its complement

Let $\angle STU = x$. Its complement is $90 - x$. Given that $x=2(90 - x)+7$.

Step2: Solve the equation for $x$

Expand the right - hand side: $x = 180-2x + 7$.
Add $2x$ to both sides: $x+2x=180 + 7$, so $3x=187$, and $x=\frac{187}{3}$.

Step3: Find the supplement of $\angle STU$

The supplement of an angle $x$ is $180 - x$. Substitute $x=\frac{187}{3}$ into the formula: $180-\frac{187}{3}=\frac{540 - 187}{3}=\frac{353}{3}=117\frac{2}{3}$.

Answer:

$117\frac{2}{3}$