In triangle ABC, angle A= 64degree. If I is the incentre of the triangle, then the measure of angle BIC is:

Options

A. a. 122degree
B. b. 120degree
C. c. 128degree
D. d. 32degree

Answer

To find the measure of angle BIC in triangle ABC where angle A = 64 degrees and I is the incenter of the triangle, we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Incenter Property**: The incenter (I) of a triangle is the point where the angle bisectors of the triangle intersect. The angle BIC can be calculated using the formula:
\[ \angle BIC = 90^\circ + \frac{1}{2} \angle A \]

2. **Substitute the Given Value**: We know that angle A = 64 degrees. Substitute this value into the formula:
\[ \angle BIC = 90^\circ + \frac{1}{2} \times 64^\circ \]

3. **Calculate Half of Angle A**: Calculate \(\frac{1}{2} \times 64^\circ\):
\[ \frac{1}{2} \times 64^\circ = 32^\circ \]

4. **Add to 90 Degrees**: Now, add this value to 90 degrees:
\[ \angle BIC = 90^\circ + 32^\circ = 122^\circ \]

5. **Final Answer**: Therefore, the measure of angle BIC is:
\[ \angle BIC = 122^\circ \]