for 2 vertical angles with measures angle 2 = (5x + 23) and angle 4 = (3x + 35), what is the measure of each angle
Vertical angles are congruent, meaning they have the same measure.
Given:
- angle 2 = 5x + 23
- angle 4 = 3x + 35
Since vertical angles are congruent, we can set the two expressions equal to each other:
5x + 23 = 3x + 35
Now, solve for x:
5x - 3x = 35 - 23
2x = 12
x = 6
Now that we have found the value of x, we can substitute it back into the expressions to find the measures of the angles:
angle 2 = 5(6) + 23 = 30 + 23 = 53
angle 4 = 3(6) + 35 = 18 + 35 = 53
So, the measure of each angle is 53 degrees.