For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)
Since vertical angles are congruent, the measure of angle 1 is equal to the measure of angle 3.
So we can set up an equation:
(2x+26)° = (3x+32)°
Now we can solve for x:
2x+26 = 3x+32
Subtract 2x from both sides:
26 = x+32
Subtract 32 from both sides:
-6 = x
Now we can find the measure of each angle by substituting x back into the expressions for the angles:
m∠1 = (2x+26)° = 2(-6)+26 = -12+26 = 14°
m∠3 = (3x+32)° = 3(-6)+32 = -18+32 = 14°
So the measure of each angle is 14°.