Question

find the measures of the labeled angles. (x + 100)° 6x° (x + 100)° = 120° (type a whole number.) 6x° = ° (type a whole number.)

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $x + 100=6x$.

Step2: Solve for $x$

Subtract $x$ from both sides: $100 = 6x−x$, which simplifies to $100 = 5x$. Then divide both sides by 5, we get $x=\frac{100}{5}=20$.

Step3: Find the measure of $6x$

Substitute $x = 20$ into $6x$, so $6x=6\times20 = 120$.

Answer:

$x = 20$, $6x=120$