Two angles are complementary. One angle has a measure of 40° and the other has a measure of (8x+2)° . What is the value of x ?(1 point)

Question

Responses

6
6

11
11

50
50

60
60

Answer 1

Two angles are complementary if their measures add up to 90°. Given that one angle measures 40° and the other measures (8x + 2)°, we can set up the equation:

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

Now, simplify the equation:

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

Combine like terms:

\[ 42 + 8x = 90 \]

Next, subtract 42 from both sides:

\[ 8x = 90 - 42 \]

Calculating the right side gives us:

\[ 8x = 48 \]

Now, divide both sides by 8:

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

Simplifying that gives:

\[ x = 6 \]

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