For two vertical angles with measures m<1 = (4x + 26) and m<3 = (3x + 32), what is the measure of each angle?
Vertical angles are opposite angles formed by the intersection of two lines. They are congruent, which means they have the same measure.
In this case, since m<1 = (4x + 26) and m<3 = (3x + 32) are vertical angles, they must have the same measure.
Setting these two expressions equal to each other, we have:
4x + 26 = 3x + 32
Subtracting 3x from both sides, we get:
4x - 3x + 26 = 32
x + 26 = 32
x = 32 - 26
x = 6
Now we can find the measure of each angle by substituting x = 6 into the expressions:
m<1 = 4x + 26 = 4(6) + 26 = 24 + 26 = 50
m<3 = 3x + 32 = 3(6) + 32 = 18 + 32 = 50
Therefore, the measure of each angle is 50 degrees.