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)

A. 11

B. 50

C. 6

D. 60

1 answer

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

Given:

  • One angle is \( 40^\circ \).
  • The other angle is \( (8x + 2)^\circ \).

Setting up the equation, we have: \[ 40 + (8x + 2) = 90 \]

Now, simplify the equation: \[ 40 + 8x + 2 = 90 \] \[ 8x + 42 = 90 \]

Next, isolate \( 8x \): \[ 8x = 90 - 42 \] \[ 8x = 48 \]

Now, divide both sides by 8: \[ x = \frac{48}{8} \] \[ x = 6 \]

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

The correct answer is C. 6.