. For two vertical 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 when two lines intersect each other, creating opposite angles.

In this case, we have two vertical angles: ∠1 and ∠3. The measure of ∠1 is given by the expression (2x + 26)°, and the measure of ∠3 is given by the expression (3x + 32)°.

Since these angles are vertical angles, they are congruent to each other. Therefore, we can set the expressions for ∠1 and ∠3 equal to each other and solve for x:

2x + 26 = 3x + 32

Subtract 2x from both sides:

26 = x + 32

Subtract 32 from both sides:

-6 = x

Now that we have found the value of x, we can substitute it back into one of the expressions to find the measure of each angle. Let's use ∠1 as an example:

∠1 = (2x + 26)°

Substituting x = -6:

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

Therefore, the measure of each vertical angle is 14°.