Angle Pairs Unit Test

Question

14 of 15 14 of 15 Items

Question
For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)
°

Answer 1

Vertical angles are congruent, which means they have the same measure. Therefore, we can set the measures of angle 1 and angle 3 equal to each other and solve for x.

m∠1 = m∠3
2x + 26 = 3x + 32

Now, we can solve this equation for x:

Subtract 2x from both sides:
26 = x + 32

Subtract 32 from both sides:
-6 = x

Now that we have the value of x, we can substitute it back into either of the angle measures to find the measure of each angle. Let's use angle 1:

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

Therefore, the measure of each angle is 14°.