For two vertical angles with measures m/2 = (5x+23) ° and m/4 = (3x +35) °, what is the measure of each angle? (1 point)
○ 6°
O 53°
O 15.3°
O 29°
We know that vertical angles are congruent, which means they have the same measure.
Let's set the measures of m/2 and m/4 equal to each other and solve for x:
m/2 = m/4
(5x + 23) = (3x + 35)
5x - 3x = 35 - 23
2x = 12
x = 12/2
x = 6
Now, let's substitute the value of x back into either equation to find the measure of the angles. Let's use m/2:
m/2 = 5x + 23
m/2 = 5(6) + 23
m/2 = 30 + 23
m/2 = 53
Therefore, the measure of each angle is 53 degrees. Answer choice:
O 53°