In a `Delta`ABC, the internal angle bisector of `angle`ABC and `angle`ACB meets at point ‘O’. If the `angle`BOC is `134^@`, then find `angle`BAC.

Options

A. a) `76^@`
B. b) `84^@`
C. c) `92^@`
D. d) `88^@`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Triangle and Given Information
We have triangle ABC with internal angle bisectors of angles ABC and ACB meeting at point O. We know that angle BOC is given as 134°.

### Step 2: Use the Angle Bisector Theorem
In triangle geometry, there is a relationship between the angles formed by the intersection of angle bisectors. Specifically, the angle BOC can be expressed in terms of angle BAC. The formula is:
\[ \angle BOC = 90^\circ + \frac{\angle BAC}{2} \]

### Step 3: Substitute the Given Value
We substitute the known value of angle BOC into the equation:
\[ 134^\circ = 90^\circ + \frac{\angle BAC}{2} \]

### Step 4: Isolate the Angle BAC
To isolate angle BAC, we first subtract 90° from both sides:
\[ 134^\circ - 90^\circ = \frac{\angle BAC}{2} \]
\[ 44^\circ = \frac{\angle BAC}{2} \]

### Step 5: Solve for Angle BAC
Next, we multiply both sides by 2 to find angle BAC:
\[ \angle BAC = 2 \times 44^\circ \]
\[ \angle BAC = 88^\circ \]

### Final Answer
Thus, the measure of angle BAC is:
\[ \angle BAC = 88^\circ \]

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