Question

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 pairs of angles that are opposite each other when two lines intersect. They are always congruent, which means they have equal measure.

So, we can set up the equation 2x + 26 = 3x + 32 to find the value of x.

Subtracting 2x from both sides, we get 26 = x + 32.

Subtracting 32 from both sides, we get -6 = x.

Now, we substitute this value of x back into either angle measure expression to find the measure of each angle.

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

So, m<1 = 14 degrees.

m<3 = 3(-6) + 32 = -18 + 32 = 14.

So, m<3 = 14 degrees.