One angle of a quadrilateral is `180^@` and the remaining three angles are equal. Find the measure of other three equal angles.

Options

A. `60^@`
B. `50^@`
C. `66^@`
D. `55^@`

Answer

To solve the problem step by step, let's follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Identify the Angles**:
- We know one angle of the quadrilateral is \(180^\circ\).
- Let the measure of the other three equal angles be \(x\) degrees.

2. **Use the Sum of Angles Property**:
- The sum of all angles in a quadrilateral is \(360^\circ\).
- Therefore, we can write the equation:
\[ 180^\circ + x + x + x = 360^\circ \]

3. **Simplify the Equation**:
- Combine the \(x\) terms:
\[ 180^\circ + 3x = 360^\circ \]

4. **Isolate \(3x\)**:
- Subtract \(180^\circ\) from both sides:
\[ 3x = 360^\circ - 180^\circ \]
- This simplifies to:
\[ 3x = 180^\circ \]

5. **Solve for \(x\)**:
- Divide both sides by \(3\):
\[ x = \frac{180^\circ}{3} \]
- This gives:
\[ x = 60^\circ \]

6. **Conclusion**:
- Each of the three equal angles in the quadrilateral measures \(60^\circ\).

### Final Answer:
The measure of the other three equal angles is \(60^\circ\).

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