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

11
11

50

Answer 1

To find the value of \( x \) when two angles are complementary, we start by remembering that complementary angles add up to \( 90^\circ \).

Given:

• The first angle measures \( 40^\circ \).
• The second angle measures \( (8x + 2)^\circ \).

We can set up the equation:

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

Now, simplify and solve for \( x \):

1. Combine like terms:

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

2. Subtract 42 from both sides:

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

3. Divide by 8:

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

Therefore, the value of \( x \) is:

\[ \boxed{6} \]