Question

For two vertical angles with measure m 1= (2x+26) degrees an m 3 = (3x+32) degrees what is the measure of each angle?

Answer 1

Vertical angles are formed by two intersecting lines and share the same vertex but are opposite to each other.

By definition, vertical angles have equal measures. So, we can set the two given angles equal to each other and solve for x:

(2x+26) = (3x+32)

To solve for x, let's isolate the x terms on one side:

2x - 3x = 32 - 26
-x = 6
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:

m1 = 2x + 26
m1 = 2(-6) + 26
m1 = -12 + 26
m1 = 14 degrees

m3 = 3x + 32
m3 = 3(-6) + 32
m3 = -18 + 32
m3 = 14 degrees

Therefore, the measure of angle m1 is 14 degrees and the measure of angle m3 is also 14 degrees.