Point 'O' is the incentre of the `DeltaPQR`. If `/_POR = 115^@`, then value of `/_PQR` is:

Options

A. `40^@`
B. `65^@`
C. `50^@`
D. `25^@`

Answer

To find the value of angle \( \angle PQR \) given that \( \angle POR = 115^\circ \) and point \( O \) is the incenter of triangle \( PQR \), we can follow these steps:

### Step 1: Understand the relationship between the angles
Since \( O \) is the incenter of triangle \( PQR \), the angle \( \angle POR \) is related to the angles of triangle \( PQR \). Specifically, the angle \( \angle POR \) is equal to \( 90^\circ + \frac{1}{2} \angle PQR \).

### Step 2: Set up the equation
From the relationship mentioned above, we can write the equation:
\[ \angle POR = 90^\circ + \frac{1}{2} \angle PQR \]
Substituting the given value of \( \angle POR \):
\[ 115^\circ = 90^\circ + \frac{1}{2} \angle PQR \]

### Step 3: Solve for \( \angle PQR \)
Now, we will isolate \( \angle PQR \):
1. Subtract \( 90^\circ \) from both sides:
\[ 115^\circ - 90^\circ = \frac{1}{2} \angle PQR \]
\[ 25^\circ = \frac{1}{2} \angle PQR \]

2. Multiply both sides by 2 to solve for \( \angle PQR \):
\[ 2 \times 25^\circ = \angle PQR \]
\[ \angle PQR = 50^\circ \]

### Conclusion
Thus, the value of \( \angle PQR \) is \( 50^\circ \).

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