PQRSTU is a cyclic hexagon. Then `/_P + /_R + /_T `is equal to

Options

A. `720^@`
B. `360^@`
C. `540^@`
D. `180^@`

Answer

To solve the problem, we need to find the sum of angles \( \angle P + \angle R + \angle T \) in the cyclic hexagon \( PQRSTU \).

### Step-by-Step Solution:

1. **Understand the Properties of a Cyclic Hexagon**:
A cyclic hexagon is a hexagon where all vertices lie on a single circle. One important property of cyclic polygons is that the sum of the interior angles can be calculated using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides. For a hexagon, \( n = 6 \).

2. **Calculate the Sum of Interior Angles**:
Using the formula:
\[ \text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \]

3. **Divide the Angles**:
In a cyclic hexagon, the sum of the angles can be divided into two groups:
\[ \angle P + \angle R + \angle T + \angle Q + \angle S + \angle U = 720^\circ \]
We can also note that the angles can be grouped as:
\[ \angle P + \angle R + \angle T = \angle Q + \angle S + \angle U \]

4. **Set Up the Equation**:
Let:
\[ \angle P + \angle R + \angle T = x \]
Then:
\[ \angle Q + \angle S + \angle U = x \]
Therefore:
\[ x + x = 720^\circ \]
Simplifying gives:
\[ 2x = 720^\circ \]

5. **Solve for \( x \)**:
Divide both sides by 2:
\[ x = \frac{720^\circ}{2} = 360^\circ \]

Thus, the sum of angles \( \angle P + \angle R + \angle T \) is equal to \( 360^\circ \).

### Final Answer:
\[ \angle P + \angle R + \angle T = 360^\circ \]