Question
d. \( x+y+2 \) e. \( x-2 y \) 9. The figure shows a line broken into 3 adjacent angles. If \( 2 y=120 \), what is the value of \( x \) ?
Ask by Peters Schmidt. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To find \( x \), we know that \( y = 60^\circ \) and the sum of the three angles is \( 180^\circ \). Therefore, \( x + 60^\circ + z = 180^\circ \). Without additional information about angle \( z \), we cannot determine the exact value of \( x \).
Solution
To find the value of \( x \) in the given figure, we need to use the information provided about the adjacent angles and the equation \( 2y = 120 \).
Given:
- The line is broken into 3 adjacent angles.
- \( 2y = 120 \)
Since the line is broken into 3 adjacent angles, the sum of these angles is \( 180^\circ \). Let's denote the three angles as \( x \), \( y \), and \( z \). Therefore, we have:
\[ x + y + z = 180^\circ \]
We are also given that \( 2y = 120 \), which means \( y = 60^\circ \).
Substitute the value of \( y \) into the equation \( x + y + z = 180^\circ \):
\[ x + 60^\circ + z = 180^\circ \]
Now, we need to find the value of \( x \) using the given information and the equation above.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the value of \( x \), we first solve for \( y \) using the equation \( 2y = 120 \). Dividing both sides by 2 gives us \( y = 60 \). Next, we can substitute \( y \) into the expressions given by the broken angles. Assuming the angles add up to form a straight line, which is \( 180^\circ \), we can set up the equation: \( x + y + 2 + x - 2y = 180^\circ \). Simplifying this gives: \( 2x - y + 2 = 180 \). Substituting \( y = 60 \) into that results in: \( 2x - 60 + 2 = 180 \) \( 2x - 58 = 180 \) \( 2x = 238 \) \( x = 119 \). So, the value of \( x \) is \( 119 \).
