Question

$\angle1$ and $\angle2$ are vertical angles. if $m\angle1=(2x - 20)^{circ}$ and $m\angle2=(x + 20)^{circ}$, then find the measure of $\angle1$.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1 = m\angle2$.
$2x−20=x + 20$

Step2: Solve for $x$

Subtract $x$ from both sides:
$2x−x−20=x−x + 20$
$x−20=20$
Then add 20 to both sides:
$x−20 + 20=20+20$
$x = 40$

Step3: Find the measure of $\angle1$

Substitute $x = 40$ into the expression for $m\angle1$:
$m\angle1=(2x−20)^{\circ}=(2\times40−20)^{\circ}$
$=(80 - 20)^{\circ}=60^{\circ}$

Answer:

$60^{\circ}$