Question
Lines AB and CD are perpendicular to each other. If 1 measures (3x + 4)°, and 2 measures 38°, what is the value of x?
A.
x = 14
B.
x = 52
C.
x = 16
D.
x = 1
Answers
GPT-4o mini
Since lines AB and CD are perpendicular to each other, the sum of their angles is 90 degrees.
Given:
- Angle 1 (measured as \( (3x + 4)^\circ \))
- Angle 2 (measured as \( 38^\circ \))
We can set up the equation based on the relationship that the two angles sum to 90 degrees:
\[
(3x + 4) + 38 = 90
\]
Now, let's simplify and solve for \( x \):
1. Combine like terms:
\[
3x + 42 = 90
\]
2. Subtract 42 from both sides:
\[
3x = 90 - 42
\]
\[
3x = 48
\]
3. Divide by 3:
\[
x = \frac{48}{3}
\]
\[
x = 16
\]
So the value of \( x \) is \( 16 \).
Thus, the correct answer is:
**C. x = 16**
Given:
- Angle 1 (measured as \( (3x + 4)^\circ \))
- Angle 2 (measured as \( 38^\circ \))
We can set up the equation based on the relationship that the two angles sum to 90 degrees:
\[
(3x + 4) + 38 = 90
\]
Now, let's simplify and solve for \( x \):
1. Combine like terms:
\[
3x + 42 = 90
\]
2. Subtract 42 from both sides:
\[
3x = 90 - 42
\]
\[
3x = 48
\]
3. Divide by 3:
\[
x = \frac{48}{3}
\]
\[
x = 16
\]
So the value of \( x \) is \( 16 \).
Thus, the correct answer is:
**C. x = 16**