Question

For two vertical angles with measures angle2=(5x+23)° and angle4=(3x+35)°, what is the measure of each angle?
step by step

Answer 1

To find the measure of each angle, we need to set the two expressions for the angles equal to each other and solve for x.

Given:
Angle 2 = (5x + 23)°
Angle 4 = (3x + 35)°

Since vertical angles are congruent, we have:
Angle 2 = Angle 4

Therefore, we can set up the equation:
5x + 23 = 3x + 35

Subtract 3x from both sides:
2x + 23 = 35

Subtract 23 from both sides:
2x = 12

Divide both sides by 2:
x = 6

Now, we can substitute the value of x back into both expressions to find the measures of the angles:
Angle 2 = (5x + 23)°
Angle 2 = (5 * 6 + 23)°
Angle 2 = (30 + 23)°
Angle 2 = 53°

Angle 4 = (3x + 35)°
Angle 4 = (3 * 6 + 35)°
Angle 4 = (18 + 35)°
Angle 4 = 53°

So, the measure of each angle is 53°.