For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)°, what is the measure of each angle?(1 point)
Since vertical angles are congruent, it means that their measures are equal.
Setting the measures of the two angles equal to each other, we have:
(5x+23)° = (3x+35)°
Now, we can solve this equation for x:
5x+23 = 3x+35
Subtracting 3x from both sides, we get:
2x+23 = 35
Subtracting 23 from both sides, we get:
2x = 12
Dividing both sides by 2, we get:
x = 6
Now that we have the value of x, we can substitute it back into either angle measure equation to find the measure of each angle. Let's use m∠2:
m∠2 = (5x+23)°
= (5*6+23)°
= (30+23)°
= 53°
Therefore, the measure of each angle is 53°.