To solve the problem, we need to understand the relationships between the angles based on their arrangement (which we can guess generally involves parallel lines, complementary angles, or angles in a triangle).
Typically, the angles would either be supplementary (add up to 180 degrees) or complementary (add up to 90 degrees). Since we don't have a visual, we'll assume they relate to a triangle or some angles sharing a vertex.
To solve for x:
Let's assume angles 1, 2, and 3 form a linear pair (or are part of an angle sum).
- Given that angle 1 is \((131 - y)\) degrees, angle 2 is \(21\) degrees, and angle 3 is \((x + 36)\) degrees.
- If we assume they add up to \(180\), we would write:
\[ (131 - y) + 21 + (x + 36) = 180 \]
This simplifies to:
\[ x + 131 - y + 21 + 36 = 180 \]
Thus:
\[ x - y + 188 = 180 \]
Rearranging gives:
\[ x - y = -8 \quad \text{(Equation 1)} \]
To solve for y:
Since angle 1 is \((131 - y)\) and we can equate it with a complementary angle (assuming angle 1 and angle 3 are supplementary or another angle property), we can set up another relationship.
If we assume angle 1 is complementary to angle 3:
\[ (131 - y) + (x + 36) = 90 \]
This simplifies to:
\[ 131 - y + x + 36 = 90 \]
Rearranging gives us:
\[ x - y + 167 = 90 \]
Thus:
\[ x - y = -77 \quad \text{(Equation 2)} \]
Now we can return to our options to find the equations listed:
Let's analyze the provided options:
A. \(21 + x + 36 = 180\) and \(131 - y = 90\)
B. \(x + 36 = 90\) and \(21 + 131 - y = 90\)
C. \(21 + x + 36 = 90\) and \(131 - y = 90\)
D. \(21 + x + 36 = 90\) and \(131 - y = 180\)
From our setup, and depending on translating our equations set up into those:
- The first part regarding \(x\) looks like it would correspond to an angle sum leading to \(90\) or \(180\).
- The second part on \(y\) would relate to either a \(90\) or set equal to another.
Based on typically equalities and \(x, y\) relations, they look like a fit to Option A considering \(angle sum = 180\) refers to:
Answer: A.
- \(21 + x + 36 = 180\)
- \(131 - y = 90\)
Now we can solve for \(x\) and \(y\):
-
\(21 + x + 36 = 180\) simplifies to: \[ x + 57 = 180 \] \[ x = 123 \]
-
\(131 - y = 90\) simplifies to: \[ 131 - 90 = y \] \[ y = 41 \]
Thus, the values are:
- \(x = 123\)
- \(y = 41\)