If I be the incentre of `DeltaABC and angleB = 70^(@) and angleC= 50^(@)`, then the magnitude of `angleBIC` is.
यदि `I DeltaABC` का अंत: केंद्र हो और `angleB = 70^(@)` और `angleC=50^(@)`, तो `angleBIC` का परिमाण है:

Options

A. `120^(@)`
B. `105^(@)`
C. `130^(@)`
D. `60^(@)`

Explanation

To find the magnitude of angle \( BIC \) in triangle \( ABC \) where \( I \) is the incenter, and given that \( \angle B = 70^\circ \) and \( \angle C = 50^\circ \), we can follow these steps:

### Step 1: Find angle \( A \)
We know that the sum of the angles in a triangle is \( 180^\circ \). Therefore, we can calculate \( \angle A \) as follows:

\[ \angle A = 180^\circ - \angle B - \angle C \]
Substituting the given values:

\[ \angle A = 180^\circ - 70^\circ - 50^\circ \]
\[ \angle A = 180^\circ - 120^\circ = 60^\circ \]

### Step 2: Use the formula for angle \( BIC \)
The formula for finding angle \( BIC \) is given by:

\[ \angle BIC = 90^\circ + \frac{1}{2} \angle A \]

### Step 3: Substitute the value of angle \( A \)
Now, substituting the value of \( \angle A \) into the formula:

\[ \angle BIC = 90^\circ + \frac{1}{2} \times 60^\circ \]
Calculating \( \frac{1}{2} \times 60^\circ \):

\[ \frac{1}{2} \times 60^\circ = 30^\circ \]

### Step 4: Calculate angle \( BIC \)
Now, adding \( 90^\circ \) and \( 30^\circ \):

\[ \angle BIC = 90^\circ + 30^\circ = 120^\circ \]

### Final Answer
Thus, the magnitude of angle \( BIC \) is:

\[ \angle BIC = 120^\circ \]

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