Two angles are complementary. One angle has a measure of 40°

Question

and the other has a measure of (8x+2)°
. What is the value of x
?(1 point)
Responses

60
60

50
50

6
6

11

Answer 1

To find the value of \( x \), we can use the definition of complementary angles. Two angles are complementary if the sum of their measures equals \( 90^\circ \).

Let the first angle be \( 40^\circ \) and the second angle be \( (8x + 2)^\circ \). We can set up the equation:

\[ 40 + (8x + 2) = 90 \]

Now, simplify the equation:

\[ 40 + 8x + 2 = 90 \] \[ 42 + 8x = 90 \]

Next, subtract 42 from both sides:

\[ 8x = 90 - 42 \] \[ 8x = 48 \]

Now, divide by 8:

\[ x = \frac{48}{8} = 6 \]

Thus, the value of \( x \) is \( 6 \).

The correct response is 6.