For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?

29°
15.3°
53°

1 answer

To find the measure of each angle, we set the two angle expressions equal to each other since vertical angles are congruent:

m∠2 = m∠4
(5x + 23)° = (3x + 35)°

Now, we solve for x:

5x + 23 = 3x + 35
2x = 12
x = 6

Now, we substitute the value of x back into the angle expressions:

m∠2 = (5x + 23)°
= (5 * 6 + 23)°
= (30 + 23)°
= 53°

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

Therefore, the measure of each angle is 53°.