Question

two adjacent angles inside a 90 degree angle. one angle measures x+4 and the other measures 3x+2 what is x

Answer 1

To find the value of \( x \), we start by noting that the two adjacent angles are inside a 90-degree angle. This means that the sum of these two angles must equal 90 degrees.

The angles are given as \( x + 4 \) and \( 3x + 2 \). Therefore, we can set up the following equation:

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

Now, we simplify the left side:

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

Combine like terms:

\[
4x + 6 = 90
\]

Next, we subtract 6 from both sides:

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

Now, divide both sides by 4:

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

Now that we have the value of \( x \), we can conclude:

\[
\boxed{21}
\]