Question

For two vertical angles m1=(4×+26)° and m3=(3×+32)°, what is the measure of each angle

Answer 1

Vertical angles are opposite each other when two lines intersect. Therefore, the measure of m1 is equal to the measure of m3.

So, we can set up an equation with the two expressions for m1 and m3:

4x + 26 = 3x + 32

To solve for x, we can subtract 3x from both sides:

x + 26 = 32

Next, we can subtract 26 from both sides:

x = 6

Now that we have the value of x, we can substitute it back into either expression to find the measure of each angle.

Using m1 = 4x + 26:

m1 = 4(6) + 26
= 24 + 26
= 50

Therefore, the measure of each angle is m1 = 50° and m3 = 50°.