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.

Answer 1

To solve for \( x \), we start by recognizing that the two adjacent angles together form a right angle, which measures \( 90^\circ \).

The measures of the two angles are given as:

• First angle: \( (x + 4)^\circ \)
• Second angle: \( (3x + 2)^\circ \)

We can set up the equation:

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

Now, we simplify and combine like terms:

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

\[ 4x + 6 = 90 \]

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

\[ 4x = 90 - 6 \]

\[ 4x = 84 \]

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

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

\[ x = 21 \]

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