Question

for two vertical angles with meausre m 2 = 5x + 23 and m 4 = 3x + 35 what is the meaure of each angles

Answer 1

To find the measures of each angle, we know that vertical angles are congruent, meaning they have the same measure.

Since angle 2 and angle 4 are vertical angles, we can set their measures equal to each other:

5x + 23 = 3x + 35

Now, we can solve for x:

5x - 3x = 35 - 23
2x = 12
x = 6

Now that we have found the value of x, we can substitute it back into either equation to find the measure of each angle:

Angle 2: 5(6) + 23 = 30 + 23 = 53 degrees
Angle 4: 3(6) + 35 = 18 + 35 = 53 degrees

Therefore, the measure of angle 2 is 53 degrees and the measure of angle 4 is 53 degrees.