Two angles of a quadrilateral are `89^@ and 113^@`. If the two angles are equal, find the equal angles.

Answer

To solve the problem step-by-step, we need to find the equal angles in a quadrilateral where two angles are given as \(89^\circ\) and \(113^\circ\).

### Step-by-Step Solution:

1. **Understand the Problem**: We know that a quadrilateral has four angles, and we are given two angles: \(89^\circ\) and \(113^\circ\). The other two angles are equal, and we will denote them as \(x\).

2. **Use the Angle Sum Property**: The sum of all interior angles of a quadrilateral is always \(360^\circ\). Therefore, we can write the equation:
\[ 89^\circ + 113^\circ + x + x = 360^\circ \]

3. **Combine Like Terms**: Simplify the left side of the equation:
\[ 89 + 113 = 202 \]
So, we can rewrite the equation as:
\[ 202 + 2x = 360 \]

4. **Isolate the Variable**: To find \(x\), we need to isolate it. First, subtract \(202\) from both sides:
\[ 2x = 360 - 202 \]
\[ 2x = 158 \]

5. **Solve for \(x\)**: Now, divide both sides by \(2\) to find the value of \(x\):
\[ x = \frac{158}{2} = 79 \]

6. **Conclusion**: The equal angles in the quadrilateral are both \(79^\circ\).

### Final Answer:
The equal angles are \(79^\circ\).