O is the incentre of `DeltaPQR and /_QPR = 50^@`, then the measure of `/_QOR` is :

Options

A. `125^@`
B. `100^@`
C. `130^@`
D. `115^@`

Answer

To find the measure of angle \( \angle QOR \) in triangle \( PQR \) where \( O \) is the incenter and \( \angle QPR = 50^\circ \), we can follow these steps:

### Step 1: Understand the properties of the incenter
The incenter \( O \) of a triangle is the point where the angle bisectors of the triangle intersect. The angles formed by the incenter with the vertices of the triangle can be calculated using the formula:
\[ \angle QOR = 90^\circ + \frac{\angle QPR}{2} \]

### Step 2: Substitute the given angle
We know that \( \angle QPR = 50^\circ \). We can substitute this value into the formula:
\[ \angle QOR = 90^\circ + \frac{50^\circ}{2} \]

### Step 3: Calculate the half of \( \angle QPR \)
Now, calculate \( \frac{50^\circ}{2} \):
\[ \frac{50^\circ}{2} = 25^\circ \]

### Step 4: Add to 90 degrees
Now, we can add this value to \( 90^\circ \):
\[ \angle QOR = 90^\circ + 25^\circ = 115^\circ \]

### Conclusion
Thus, the measure of \( \angle QOR \) is:
\[ \angle QOR = 115^\circ \]