Question

For two vertical angles with measures, m<1 =(2x+26) and m<3 = (3x+32)

What is the measure of each angle

Answer 1

[AI-generated answer — Bot GPT 3.5]

Vertical angles are formed when two lines intersect. These angles are congruent, which means they have the same measure.

Thus, we can set up the equation:

m<1 = m<3

2x + 26 = 3x + 32

To solve for x, we can subtract 2x from both sides:

26 = x + 32

Next, we can subtract 32 from both sides:

-6 = x

Now, we substitute this value back into one of the expressions 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 angle 1 (m<1) is 14 degrees. Since vertical angles are congruent, the measure of angle 3 (m<3) is also 14 degrees.