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