Two complementary angles have measures (2x)° and (3x)°. What is the value of x and the two angle measures?
x= __, (2x)°= __°, and (3x)°= __°
To determine the value of x, we need to set up an equation using the fact that the two angles are complementary (meaning they add up to 90 degrees):
(2x)° + (3x)° = 90°
Combining like terms on the left side of the equation:
5x° = 90°
Now, we can solve for x by dividing both sides of the equation by 5:
x = 90° / 5 = 18°
Therefore, x is equal to 18 degrees.
We can now substitute this value back into the original expressions to find the angle measures:
(2x)° = 2 * 18° = 36°
(3x)° = 3 * 18° = 54°
So, the two angle measures are 36° and 54°.