if two adjacent angles with measures (x+18) and x are inside a 90 degree angle what is the equation for the two adjacent angles

1 answer

If the two adjacent angles are inside a 90-degree angle, their measures will sum up to 90 degrees. Given the measures of the two angles as \( (x + 18) \) and \( x \), we can set up the equation as follows:

\[ (x + 18) + x = 90 \]

Simplifying the equation:

\[ 2x + 18 = 90 \]

To isolate \( x \), subtract 18 from both sides:

\[ 2x = 90 - 18 \] \[ 2x = 72 \]

Now, divide both sides by 2:

\[ x = 36 \]

So, the measure of the first angle is \( x + 18 = 36 + 18 = 54 \) degrees, and the measure of the second angle is \( x = 36 \) degrees. The two angles are \( 54^\circ \) and \( 36^\circ \), which add up to \( 90^\circ \) as expected.

Therefore, the equation for the two adjacent angles is:

\[ (x + 18) + x = 90 \]