https://file.aiquickdraw.com/mathbot/file/1726641760614x3ca4due.jpg

The problem provided in the image includes a triangle with the following knowns:

1. \( x \), \( y \), \( a \), \( b \), and \( c \) are angles related to the triangle.
2. The summation of \( x \) and \( y \) is given as 205°.
3. We are tasked with finding the summation of \( a \) and \( b \), as well as the value of \( c \).

### Analysis:
- Since \( x \) and \( y \) are angles on a straight line, they must satisfy the linear pair rule, i.e., the sum of angles on a straight line is 180°.
- Therefore, the following relationships hold:
  \[
  a = 180^\circ - x \quad \text{and} \quad b = 180^\circ - y
  \]

- The interior angle of the triangle is:
  \[
  a + b + c = 180^\circ
  \]

Now, let's solve for the required angles using this information.

### Step-by-step Solution:
1. \( x + y = 205^\circ \) is given.
2. From the straight-line property:
   \[
   a = 180^\circ - x \quad \text{and} \quad b = 180^\circ - y
   \]
3. Adding \( a \) and \( b \):
   \[
   a + b = (180^\circ - x) + (180^\circ - y

In the figure below, if the summation of x and y is 205°, then find out the summation of a and b. Then find the value of c.

Solve a triangle angle sum problem where the sum of x and y is 205°. Learn how to apply geometry concepts like the sum of angles on a straight line and triangle interior angle sum theorem to find the summation of angles a and b, as well as the value of angle c.

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