The value of two angles of a quadrilateral is `65^(@)` cach. The other two angles are also equal. Find out the value of these angles.

Options

A. `125^(@)`
B. `115^(@)`
C. `105^(@)`
D. `100^(@)`

Answer

To find the value of the two equal angles in the quadrilateral, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angles**: We are given that two angles of the quadrilateral are each \(65^\circ\). Let the other two equal angles be \(x\) each. So, we have:
\[ \text{Angles: } 65^\circ, 65^\circ, x, x \]

2. **Use the Sum of Angles in a Quadrilateral**: The sum of all interior angles in a quadrilateral is \(360^\circ\). Therefore, we can set up the equation:
\[ 65 + 65 + x + x = 360 \]

3. **Simplify the Equation**: Combine the known angles:
\[ 130 + 2x = 360 \]

4. **Isolate the Variable**: Subtract \(130\) from both sides:
\[ 2x = 360 - 130 \]
\[ 2x = 230 \]

5. **Solve for \(x\)**: Divide both sides by \(2\):
\[ x = \frac{230}{2} = 115 \]

6. **Conclusion**: The value of each of the other two angles is:
\[ x = 115^\circ \]

### Final Answer:
The value of the other two angles in the quadrilateral is \(115^\circ\) each.

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