Question

for two vertical angles with measures m- angle 2 = (5x + 23)° and m-angle 4 = (3x + 35)°, what is the measure of each angle?
A 29°
B 53°
C 6°
D 15.3°

Answer 1

To find the measure of each angle, we need to remember that vertical angles are congruent, meaning they have the same measure.

So, set the two expressions equal to each other:
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, substitute x back into one of the expressions to find the measure of each angle:
Angle 2 = 5(6) + 23 = 53°
Angle 4 = 3(6) + 35 = 53°

Therefore, the measure of each angle is 53°.

Answer: B 53°