for two vertical angles with measures 1 = (2x + 26) and 3 = (3x + 32), what is the measure of each angle?

Answer 1

Vertical angles are formed by two intersecting lines and are always congruent. Therefore, since angle 1 and angle 3 are vertical angles, their measures must be equal.

Setting the expressions for the two angles equal to each other, we have:

2x + 26 = 3x + 32

Subtracting 2x from both sides gives:

26 = x + 32

Subtracting 32 from both sides gives:

-6 = x

Therefore, x = -6.

Substituting this value for x into the expression for angle 1, we have:

1 = 2(-6) + 26
1 = -12 + 26
1 = 14

Therefore, the measure of angle 1 is 14 degrees.

Substituting x = -6 into the expression for angle 3, we have:

3 = 3(-6) + 32
3 = -18 + 32
3 = 14

Therefore, the measure of angle 3 is 14 degrees.

So, each angle measures 14 degrees.