For two vertical angles with measures m<2 = (5x + 23) degree and m<4 = (3x + 35) degree, what is the measure of each angle?

Question

Options:
15.3 degree
53 degree
29 degree
6 degree

Answer 1

To find the measure of each angle, we need to set their measures equal to each other because vertical angles are congruent.

So, we have the equation:
5x + 23 = 3x + 35

Subtracting 3x from both sides, we get:
2x + 23 = 35

Subtracting 23 from both sides, we obtain:
2x = 12

Dividing both sides by 2, we find:
x = 6

Now, we can substitute x = 6 back into either equation to find the measure of the angles. Let's use the first equation:

m<2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53 degrees

m<4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53 degrees

Therefore, the measure of each angle is 53 degrees.