For two vertical angles with measures m∠1 = (4x + 26) °

Question

and m∠3 = (3x + 32) °
, what is the measure of each angle?(1 point)
Responses

6°
6degree

24°
24degree

50°
50degree

64°
64degree

Answer 1

To find the measure of each angle, we can set the two angle measures equal to each other.

m∠1 = m∠3

(4x + 26) ° = (3x + 32) °

Now, let's solve for x:

4x + 26 = 3x + 32

Subtract 3x from both sides:

x + 26 = 32

Subtract 26 from both sides:

x = 6

Now that we have the value of x, we can substitute it back into either equation to find the measure of the angles. Let's substitute it into m∠1:

m∠1 = (4x + 26) °

m∠1 = (4(6) + 26) °

m∠1 = (24 + 26) °

m∠1 = 50 °

Therefore, m∠1 is equal to 50°.

To find the measure of m∠3, we can substitute x = 6 back into the equation:

m∠3 = (3x + 32) °

m∠3 = (3(6) + 32) °

m∠3 = (18 + 32) °

m∠3 = 50 °

Therefore, m∠3 is also equal to 50°.

The correct answer is:

m∠1 = 50°
m∠3 = 50°