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

Question

50

11

6

60

Answer 1

Complementary angles are two angles that add up to 90 degrees. Given that one angle measures 40 degrees and the other measures \(8x + 2\), we can set up the following equation:

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

Now, simplify the equation:

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

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.