Question
Two complementary angles have measures (2x)° and (3x)°. What is the value of x and the two angle measures?
x= __, (2x)°= __°, and (3x)°= __°
x= __, (2x)°= __°, and (3x)°= __°
Answers
GPT 3.5
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°.
(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°.