
**a.** What is the value of​ x?

**b.** What is the value of​ y?

**c.** The chair can lay farther back so that the 

70degrees° 

angle changes to 

86degrees° 

and 

xdegrees° 

changes to 

36degrees°. 

How does this affect the 

119degrees° 

​angle?

Let's break down each part of the problem systematically.

### Part **a**: What is the value of \( x \)?

You haven't provided an equation or context for \( x \). This might refer to an angle or some other value related to a chair. Please clarify if it's part of a geometric setup (such as angles in a triangle) or another equation.

### Part **b**: What is the value of \( y \)?

Similarly, the value of \( y \) depends on the context or equation. Please provide more details or a diagram for a more specific answer.

### Part **c**: The chair can lay farther back so that:
- The \( 70^\circ \) angle changes to \( 86^\circ \).
- The \( x^\circ \) angle changes to \( 36^\circ \).

You asked how this affects the \( 119^\circ \) angle. Assuming we're working with a triangle (perhaps the angles around the chair forming a triangle), we can apply the angle sum property of a triangle, which states that the sum of the internal angles of a triangle is always \( 180^\circ \).

#### Before Adjustment:
If the triangle's angles are \( 70^\circ \), \( x^\circ \), and \( 119^\circ \), we can find \( x \) using the equation:
\[
70^\circ + 119^\circ + x^\circ = 180^\circ
\]
\[
189^\circ + x^\circ = 180^\circ
\]
\[
x^\circ = 180^\circ - 189^\circ = -9^\circ
\]
This would imply that there is no valid triangle before adjustment, meaning more context is needed, as negative angles aren't physically meaningful here.

#### After Adjustment:
The angles are \( 86^\circ \), \( 36^\circ \), and the unknown angle (let's call it \( A \)). Applying the angle sum property again:
\[
86^\circ + 36^\circ + A^\circ = 180^\circ
\]
\[
122^\circ + A^\circ = 180^\circ
\]
\[
A^\circ = 180^\circ - 122^\circ = 58^\circ
\]
So, after the chair lays farther back, the \( 119^\circ \) angle would decrease to \( 58^\circ \).

### Summary:
- **Part a**: Clarify context for \( x \).
- **Part b**: Clarify context for \( y \).
- **Part c**: The \( 119^\circ \) angle changes to \( 58^\circ \) when the other angles adjust as specified.

Would you like more details or clarifications?

### Further Questions:
1. Is this problem based on geometry involving a triangle?
2. Could you describe the diagram or setup of the chair angles more clearly?
3. How were the angles initially measured in the chair problem?
4. Is there any context for the missing \( x \) and \( y \) values?
5. Would you like help solving the problem with more precise figures?

### Tip:
Remember, the sum of the interior angles of any triangle is always \( 180^\circ \), which is often useful in geometry problems!

What is the value of x? What is the value of y? The chair can lay farther back so that the 70° angle changes to 86° and x° changes to 36°. How does this affect the 119° angle?

This problem explores the effect of changing angles in a triangle, where a 70° angle shifts to 86° and x° becomes 36°. Using the Triangle Angle Sum Theorem, we determine the impact on the 119° angle, which decreases to 58°. A step-by-step solution is provided for students in Grades 7-10.

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