Question

$\angle1$ and $\angle2$ are vertical angles. if $m\angle1=(5x + 5)^{circ}$ and $m\angle2=(3x + 23)^{circ}$, then find the measure of $\angle1$.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $5x + 5=3x + 23$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $5x-3x + 5=3x-3x + 23$, which simplifies to $2x+5 = 23$. Then subtract 5 from both sides: $2x+5 - 5=23 - 5$, giving $2x=18$. Divide both sides by 2: $x=\frac{18}{2}=9$.

Step3: Find the measure of $\angle1$

Substitute $x = 9$ into the expression for $m\angle1$. So, $m\angle1=(5\times9 + 5)^{\circ}=(45 + 5)^{\circ}=50^{\circ}$.

Answer:

$50^{\circ}$