For two vertical angles with measures m 2 = (5x + 23) " and m 4 = (3x + 35)°, what is the measure of each angle? (1 point)
• 6°
• 15.3
• 53
• 29°
The measure of vertical angles is always equal. Therefore, we can set up the following equation:
m2 = m4
(5x + 23) = (3x + 35)
Simplifying the equation:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
2x + 23 = 35
Subtracting 23 from both sides:
2x = 12
Dividing both sides by 2:
x = 6
Now that we know the value of x, we can substitute it back into the expressions for m2 and m4:
m2 = (5x + 23)
= (5*6 + 23)
= 30 + 23
= 53
m4 = (3x + 35)
= (3*6 + 35)
= 18 + 35
= 53
Thus, the measure of each angle is 53°.