For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)°, what is the measure of each angle?(1 point)
Responses
6°
6 degrees
53°
53 degrees
15.3°
15.3 degrees
29°
To find the measure of each angle, we can set up an equation. Since vertical angles are congruent, we can set the measures of the two angles equal to each other:
m∠2 = m∠4
(5x+23)° = (3x+35)°
Now we can solve for x. Subtracting 3x from both sides gives:
5x+23 - 3x = 3x+35 - 3x
2x+23 = 35
Subtracting 23 from both sides gives:
2x+23 - 23 = 35 - 23
2x = 12
Dividing both sides by 2 gives:
2x/2 = 12/2
x = 6
Now we can find the measure of each angle by substituting x = 6 into the expressions:
m∠2 = (5x+23)°
m∠2 = (5(6)+23)°
m∠2 = (30+23)°
m∠2 = 53°
m∠4 = (3x+35)°
m∠4 = (3(6)+35)°
m∠4 = (18+35)°
m∠4 = 53°
Therefore, the measure of each angle is 53 degrees.