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 formed by two intersecting lines. They are congruent, which means they have the same measure.
Therefore, we can equate the two expressions:
2x + 26 = 3x + 32
To solve for x, subtract 2x from both sides:
26 = x + 32
Then subtract 32 from both sides:
-6 = x
To find the measure of each angle, substitute the value of x back into the expressions:
m∠1 = 2x + 26 = 2(-6) + 26 = 14°
m∠3 = 3x + 32 = 3(-6) + 32 = 14°
Therefore, the measure of each angle is 14°.