Question

Two adjacent angles are inside a 90°
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 \( \boxed{21} \).