For two verticle angles with measures m<1=(2x+26) and m<3=(3x+32) what is the measure of each angle?

1 answer

Vertical angles are formed by two intersecting lines and are always congruent. Therefore, we can set up an equation and solve for x to find the value of each angle.

Since vertical angles are congruent, we have:

m<1 = m<3

(2x + 26) = (3x + 32)

Rearranging to isolate terms with x:

2x - 3x = 32 - 26

-x = 6

Dividing both sides by -1 to solve for x:

x = -6

Now we can substitute x back into either m<1 or m<3 to find the measure of each angle. Let's use m<1:

m<1 = 2x + 26 = 2(-6) + 26 = -12 + 26 = 14

Therefore, the measure of angle 1 (<1) is 14 degrees.

Since vertical angles are congruent, the measure of angle 3 (<3) is also 14 degrees.