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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

65
65

13

1 answer

To solve for the value of \( x \) in this problem, we note that the two angles are complementary, meaning they add up to 90 degrees.

Given:

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

We can set up the equation:

\[ 25 + 5x = 90 \]

Now, subtract \( 25 \) from both sides:

\[ 5x = 90 - 25 \] \[ 5x = 65 \]

Next, divide both sides by \( 5 \):

\[ x = \frac{65}{5} \] \[ x = 13 \]

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

The correct response is: 13