Question

For two vertical angles where <2 = 5x + 23 degrees and < 4 = 3x + 35 degrees what is the measure of each angle

Answer 1

Vertical angles are always congruent, which means they have the same measure. Therefore, we can set the two expressions for the angles equal to each other and solve for x:

5x + 23 = 3x + 35

2x = 12

x = 6

Now that we know x, we can substitute it back into either expression to find the measure of each angle:

<2 = 5x + 23 = 5(6) + 23 = 53 degrees

<4 = 3x + 35 = 3(6) + 35 = 53 degrees

Therefore, each angle measures 53 degrees.