Question

find the measures of the labeled angles. (x + 99)° 4x° (x + 99)° = 133° (type a whole number.) 4x° = □° (type a whole number.)

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $x + 90=4x$.

Step2: Solve for x

Subtract $x$ from both sides: $90 = 4x−x$, which simplifies to $90 = 3x$. Then divide both sides by 3: $x=\frac{90}{3}=30$.

Step3: Find the measure of $4x$

Substitute $x = 30$ into $4x$. So, $4x=4\times30 = 120$.

Answer:

$(x + 90)^{\circ}=120^{\circ}$
$4x^{\circ}=120^{\circ}$