Question
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)
°
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)
°
Answers
GPT-4o mini
To solve for \(x\), we start by using the fact that the two adjacent angles sum up to 90°.
The measures of the two angles are given as:
- Angle 1: \((x + 4)^\circ\)
- Angle 2: \((3x + 2)^\circ\)
Setting up the equation:
\[
(x + 4) + (3x + 2) = 90
\]
Now simplify the left side:
\[
x + 4 + 3x + 2 = 90
\]
\[
4x + 6 = 90
\]
Next, we will isolate \(4x\):
\[
4x = 90 - 6
\]
\[
4x = 84
\]
Now, divide by 4 to solve for \(x\):
\[
x = \frac{84}{4} = 21
\]
Thus, the value of \(x\) is \(21\).
Therefore, the answer is:
\[
\boxed{21}
\]
The measures of the two angles are given as:
- Angle 1: \((x + 4)^\circ\)
- Angle 2: \((3x + 2)^\circ\)
Setting up the equation:
\[
(x + 4) + (3x + 2) = 90
\]
Now simplify the left side:
\[
x + 4 + 3x + 2 = 90
\]
\[
4x + 6 = 90
\]
Next, we will isolate \(4x\):
\[
4x = 90 - 6
\]
\[
4x = 84
\]
Now, divide by 4 to solve for \(x\):
\[
x = \frac{84}{4} = 21
\]
Thus, the value of \(x\) is \(21\).
Therefore, the answer is:
\[
\boxed{21}
\]