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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

10
10

13
13

65
65

50

1 answer

To solve for the value of \( x \) in the scenario described, we need to set up the equation based on the fact that complementary angles add up to 90 degrees.

The two angles given are:

  1. \( 25 \) degrees
  2. \( 5x \) degrees

We can write the equation as: \[ 25 + 5x = 90 \]

Now, we solve for \( x \):

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

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

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

The correct response is: 13