Question

For two vertical angles with measures two equals 5X +23 and M4 equals 3X +35 what is the measure of each angle

Answer 1

Vertical angles are formed when two lines intersect. They are opposite angles from each other, and therefore have equal measures.

Let's assume that the measure of the two vertical angles is equal to "m".

According to the given information, we have:
1) The measure of the first vertical angle is 5x + 23.
2) The measure of the fourth angle (let's call it angle M4) is 3x + 35.

Since the measure of two vertical angles is equal, we can set up the following equation:

5x + 23 = 3x + 35

By subtracting 3x from both sides of the equation, we get:

5x - 3x + 23 = 3x - 3x + 35
2x + 23 = 35

Next, we subtract 23 from both sides of the equation:

2x + 23 - 23 = 35 - 23
2x = 12

Finally, by dividing both sides of the equation by 2, we find:

2x/2 = 12/2
x = 6

Now that we have the value of x, we can substitute it back into either of the original equations to find the measure of each angle.

Let's use the first equation:

5x + 23 = 5*6 + 23
5x + 23 = 30 + 23
5x + 23 = 53

Therefore, the measure of each angle is 53.