Use the image to answer the question.
An illustration shows a right angle. A ray extends from the right angle to create complementary angles. One angle measures 25 degrees. The other angle measures 5 x degrees. The angles are not labeled.
Solve for the value of x.
(1 point)
Responses
10
10
65
65
50
50
13
The given information states that one of the angles measures 25 degrees and the other angle measures 5x degrees. Since the two angles are complementary, their sum is equal to 90 degrees.
Let's set up the equation to solve for x:
25 + 5x = 90
Now, subtract 25 from both sides of the equation:
5x = 90 - 25
5x = 65
Finally, divide both sides of the equation by 5 to solve for x:
x = 65/5
Hence, the value of x is 13.
Therefore, the correct answer is 13.
What are the two angle measures of complementary angles expressed as 3x° and (2x−5)° ?(1 point)
Responses
19° and 71°
19 degrees and 71 degrees
30° and 60°
30 degrees and 60 degrees
33° and 57°
33 degrees and 57 degrees
21° and 69°
21 degrees and 69 degrees
To find the two angle measures, we need to set up an equation using the given expressions for the angles:
First angle: 3x°
Second angle: (2x - 5)°
Since the angles are complementary, their sum is equal to 90 degrees.
Setting up the equation:
3x + (2x - 5) = 90
Combining like terms:
5x - 5 = 90
Adding 5 to both sides of the equation:
5x = 95
Dividing both sides of the equation by 5:
x = 19
Now we substitute this value of x back into the expressions for the angles:
First angle: 3(19)° = 57°
Second angle: (2(19) - 5)° = 33°
Therefore, the two angle measures of the complementary angles are 57° and 33°.
Hence, the correct answer is 57° and 33°.