Two adjacent angles are inside a 90°

Question

angle. One angle has a measure of (x+4)°
and the other angle has a measure of (3x+2)°
. What is x
?

A 90 degree angle is shown on a white background. A ray is splitting the 90 degree angle into two adjacent angles. The top angle is labeled as x plus 4. The bottom angle is labeled as 3 times x plus 2.

(1 point)

Answer 1

To find the value of \( x \) for the two adjacent angles that sum up to \( 90^\circ \), we can set up the equation:

\[ (x + 4) + (3x + 2) = 90 \]

Now, combine like terms:

\[ x + 4 + 3x + 2 = 90 \] \[ 4x + 6 = 90 \]

Next, subtract 6 from both sides:

\[ 4x = 84 \]

Now, divide both sides by 4:

\[ x = 21 \]

Thus, the value of \( x \) is \( \boxed{21} \).