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∠1 and ∠2 are vertical angles. if m∠1=(4x + 2)° and m∠2=(x + 17)°, then find the measure of
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Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1 = m\angle2$.
$(4x + 2)^{\circ}=(x + 17)^{\circ}$

Step2: Solve the equation for $x$

Subtract $x$ from both sides:
$4x+2 - x=x + 17 - x$
$3x+2 = 17$
Subtract 2 from both sides:
$3x+2-2=17 - 2$
$3x=15$
Divide both sides by 3:
$\frac{3x}{3}=\frac{15}{3}$
$x = 5$

Step3: Find the measure of the angles

Substitute $x = 5$ into the expression for $m\angle2$ (we could also use the expression for $m\angle1$).
$m\angle2=(x + 17)^{\circ}$
$m\angle2=(5 + 17)^{\circ}=22^{\circ}$

Answer:

$22$