Use the image to answer the question.

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

50
50

10
10

13
13

65
65

Answer 1

To find the value of \( x \), we can use the fact that the two angles are complementary. This means that their measures add up to 90 degrees.

Let's denote the given angles:

• One angle is \( 25 \) degrees.
• The other angle is \( 5x \) degrees.

We can set up the equation: \[ 25 + 5x = 90 \]

Now, we can solve for \( x \):

1. Subtract \( 25 \) from both sides: \[ 5x = 90 - 25 \] \[ 5x = 65 \]

2. Divide both sides by \( 5 \): \[ x = \frac{65}{5} \] \[ x = 13 \]

Thus, the value of \( x \) is \( 13 \).

The correct response is: 13