For two vertical angles with measures m/2 = (5x + 23) ° and m<4 = (3x + 35) • , what is the measure of each angle? (1 point)
Vertical angles are formed when two lines intersect. These angles are congruent, meaning they have the same measure.
Therefore, m/2 = m<4, which gives us:
(5x + 23)° = (3x + 35)°
Now we can solve for x:
5x + 23 = 3x + 35
Subtract 3x from both sides:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide by 2:
x = 6
Now that we have the value of x, we can find the measure of each angle:
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°.