14) For two vertical angles with measures m<1 = (2x +26)° and m<3 = (3x +32)°, what is the measure of each angle? (make sure to include units with your answer)
The measure of angle 1 is (2x + 26)° and the measure of angle 3 is (3x + 32)°.
Since vertical angles are congruent, we can set these two expressions equal to each other:
2x + 26 = 3x + 32
Subtracting 2x from both sides:
26 = x + 32
Subtracting 32 from both sides:
x = -6
Now, we can substitute x back into either expression to find the measure of each angle:
m<1 = (2(-6) + 26)
m<1 = (12 + 26)
m<1 = 38°
m<3 = (3(-6) + 32)
m<3 = (-18 + 32)
m<3 = 14°
Therefore, the measure of angle 1 is 38° and the measure of angle 3 is 14°.