A figure shows two nonadjacent angles with measures (2x+3)° and 2x° . If the angles are complementary, what is the equation for the angle measures?
Since two angles are complementary, the sum of their measures must equal 90 degrees.
Therefore, we have the equation:
(2x+3) + 2x = 90
Simplifying this equation, we combine like terms:
4x + 3 = 90
Next, subtract 3 from both sides of the equation to isolate 4x:
4x = 87
Finally, divide both sides of the equation by 4 to solve for x:
x = 21.75
Therefore, the equation for the angle measures is:
(2x+3)° = (2(21.75)+3)° = 45.5°
2x° = 2(21.75)° = 43.5°