The bisector of an angle is produced backwards .It bisects which angle at the same vertex ?

Options

A. acute
B. obtuse
C. reflex
D. complete

Answer

To solve the problem step by step, we need to understand the concept of angle bisectors and how they relate to the angles they bisect.

### Step-by-Step Solution:

1. **Understanding the Angle Bisector**:
- An angle bisector is a line that divides an angle into two equal parts. For example, if we have an angle of 90 degrees, the bisector will create two angles of 45 degrees each.

2. **Assuming an Angle**:
- Let’s assume we have an angle ∠AOB which measures 90 degrees. The bisector of this angle will divide it into two equal angles of 45 degrees each.

3. **Drawing the Bisector**:
- Draw the angle ∠AOB and then draw the bisector line OC from point O such that it divides ∠AOB into two equal angles (45 degrees each).

4. **Producing the Bisector Backwards**:
- Now, if we extend the bisector line OC backwards, we denote the new point as A'. This means we are considering the angle A'OA.

5. **Finding the Measure of Angle A'OA**:
- Since AOB is 90 degrees, the straight line A'OA will measure 180 degrees. Therefore, we can say:
\[ \text{Angle A'OA} = \text{Angle AOB} + \text{Angle BOC} \]
\[ 180^\circ = 45^\circ + x \]
- Here, x is the angle we need to find, which is the angle A'OA.

6. **Calculating the Value of x**:
- Rearranging the equation gives:
\[ x = 180^\circ - 45^\circ = 135^\circ \]

7. **Identifying the Type of Angle**:
- Now we have found that the angle A'OA measures 135 degrees. This angle is classified as an obtuse angle since it is greater than 90 degrees but less than 180 degrees.

8. **Finding the Angle Bisected by the Extended Bisector**:
- The angle AOC (which is the angle formed by the bisector) is 135 degrees. The total angle formed by the extended bisector A'OA is:
\[ 135^\circ + 135^\circ = 270^\circ \]
- Since this angle is greater than 180 degrees, it is classified as a reflex angle.

9. **Conclusion**:
- Therefore, the bisector of the angle AOB, when produced backwards, bisects a reflex angle of 270 degrees.

### Final Answer:
The bisector of an angle produced backwards bisects a reflex angle.