For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?
Vertical angles are always congruent, which means they have the same measure. Therefore, we can set the measures of the two vertical angles equal to each other and solve for x.
m∠1 = m∠3
(2x + 26) = (3x + 32)
Now, solve for x:
2x + 26 = 3x + 32
2x - 3x = 32 - 26
-x = 6
x = -6
Now that we have found the value of x, we can substitute it back into either of the angle measures to find the actual measure of each angle.
m∠1 = 2(-6) + 26 = -12 + 26 = 14°
m∠3 = 3(-6) + 32 = -18 + 32 = 14°
Therefore, the measure of each angle is 14°.