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

6
6

50
50

11

Answer 1

Two angles are complementary if the sum of their measures is equal to 90°.

Let the first angle be 40° and the second angle be \( (8x + 2)° \).

The equation for complementary angles can be set up as follows:

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

Now, combine like terms:

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

This simplifies to:

\[ 42 + 8x = 90 \]

Next, subtract 42 from both sides:

\[ 8x = 90 - 42 \]

\[ 8x = 48 \]

Now, divide both sides by 8:

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

\[ x = 6 \]

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