Question For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)

Answer 1

To find the measure of each angle, we need to set up an equation based on the fact that vertical angles are congruent.

Vertical angles are equal in measure, so we have:
m∠1 = m∠3

(2x+26)° = (3x+32)°

Now, we can solve for x:
2x + 26 = 3x + 32
26 - 32 = 3x - 2x
-6 = x

Now that we have found the value of x, we can substitute it back into the expressions for each angle to find their measures:

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°.