For two vertical angles with measures m∠1=(2x+26)°

Question

and m∠3=(3x+32)°
, what is the measure of each angle?

Answer 1

To find the measures of each angle, we set up an equation where the vertical angles are equal to each other.

m∠1 = m∠3
(2x + 26)° = (3x + 32)°

Now, we solve for x:

2x + 26 = 3x + 32
26 - 32 = 3x - 2x
-6 = x

Now that we have found x, we can substitute it back into either equation to find the measure of each angle.

m∠1 = 2(-6) + 26 = -12 + 26 = 14°
m∠3 = 3(-6) + 32 = -18 + 32 = 14°

Therefore, the measure of angle m∠1 is 14° and the measure of angle m∠3 is 14°.