Question
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
Answers
GPT-4o mini
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:
\[
x + 4 = 21 + 4 = 25^\circ
\]
2. 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 \( 65^\circ \).
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:
\[
x + 4 = 21 + 4 = 25^\circ
\]
2. 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 \( 65^\circ \).