For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)
°
To find the measures of the vertical angles, we need to set them equal to each other and solve for x.
m∠1 = m∠3
2x + 26 = 3x + 32
Next, we subtract 2x and 32 from both sides to isolate the variable x.
26 - 32 = 3x - 2x
-6 = x
Now that we have the value of x, we can substitute it back into one of the angle measures to find the measure of each angle.
m∠1 = 2x + 26
m∠1 = 2(-6) + 26
m∠1 = -12 + 26
m∠1 = 14°
m∠3 = 3x + 32
m∠3 = 3(-6) + 32
m∠3 = -18 + 32
m∠3 = 14°
Therefore, the measure of each angle is 14°.