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

1 answer

To solve for \( x \) and the two unknown angles inside a \( 90^\circ \) angle, we start by setting up an equation based on the information provided.

The equation will be:

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

Now, simplify and combine like terms:

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

Next, subtract 6 from both sides to isolate the term with \( x \):

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

Now, divide both sides by 4 to solve for \( x \):

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

Now that we have \( x \), we can find the measurements of the two angles.

  1. The first angle is:

\[ x + 4 = 21 + 4 = 25^\circ \]

  1. The second angle is:

\[ 3x + 2 = 3(21) + 2 = 63 + 2 = 65^\circ \]

Thus, the solution is:

  • \( x = 21 \)
  • The two angles are \( 25^\circ \) and \( 65^\circ \).