If O is the orthocentre of a triangle `ABC `and `/_BOC = 100^@`, the measure of `/_BAC` is

Options

A. `100^@`
B. `180^@`
C. `80^@`
D. `200^@`

Answer

To find the measure of angle \( \angle BAC \) in triangle \( ABC \) where \( O \) is the orthocenter and \( \angle BOC = 100^\circ \), we can use the property of the angles related to the orthocenter.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We know that \( O \) is the orthocenter of triangle \( ABC \).
- We are given that \( \angle BOC = 100^\circ \).

2. **Use the Property of Angles at the Orthocenter**:
- A key property of the angles in a triangle involving the orthocenter states that:
\[ \angle BOC + \angle BAC = 180^\circ \]
- This means that the sum of the angle \( BOC \) and the angle \( BAC \) is equal to \( 180^\circ \).

3. **Substitute the Known Value**:
- We can substitute the known value of \( \angle BOC \) into the equation:
\[ 100^\circ + \angle BAC = 180^\circ \]

4. **Solve for \( \angle BAC \)**:
- Rearranging the equation to find \( \angle BAC \):
\[ \angle BAC = 180^\circ - 100^\circ \]
\[ \angle BAC = 80^\circ \]

5. **Conclusion**:
- Therefore, the measure of \( \angle BAC \) is \( 80^\circ \).

### Final Answer:
The measure of \( \angle BAC \) is \( 80^\circ \).

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