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 \( x \), we start by using the fact that the two angles are adjacent and together they form a \( 90^\circ \) angle. This means that:

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

Now we can combine like terms:

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

This simplifies to:

\[ 4x + 6 = 90 \]

Next, we will isolate \( 4x \) by subtracting \( 6 \) from both sides:

\[ 4x = 90 - 6 \] \[ 4x = 84 \]

Now, divide both sides by \( 4 \):

\[ x = \frac{84}{4} \] \[ x = 21 \]

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