For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)°, what is the measure of each angle?(1 point)
°
Vertical angles are always congruent, which means they have the same measure. Therefore, the measure of angle 1 and angle 3 are equal.
m∠1 = m∠3
(2x + 26)° = (3x + 32)°
To solve for x, subtract 2x from both sides:
26° = (3x + 32)° - (2x)°
26° = x + 32°
Next, subtract 32° from both sides:
-6° = x
Now that we have the value of x, we can substitute it into either angle measure to find the measure of each angle. Let's use m∠1:
m∠1 = (2x + 26)°
m∠1 = (2(-6) + 26)°
m∠1 = (-12 + 26)°
m∠1 = 14°
Therefore, the measure of each angle is 14°.