Explanation:

To understand why the angle between the bisectors of two adjacent supplementary angles is a right angle, we need to first understand what a bisector is and what supplementary angles are.

Bisector:
A bisector is a line or a ray that divides an angle into two congruent angles. In other words, it divides the angle into two equal parts.

Supplementary Angles:
Supplementary angles are two angles that add up to 180 degrees. In other words, the sum of the measures of two supplementary angles is 180 degrees.

Now, let's consider two adjacent supplementary angles, which means they share a common side. Let's call these angles ∠ABC and ∠CBD. The bisectors of these angles are lines or rays that divide each of the angles into two equal parts.

Proof:
1. Let the bisector of ∠ABC be line AD and the bisector of ∠CBD be line CE.
2. Since AD bisects ∠ABC, it divides the angle into two congruent angles, ∠ABD and ∠CBD.
3. Similarly, CE bisects ∠CBD, dividing it into two congruent angles, ∠CBE and ∠DBE.
4. Now, since ∠ABD and ∠CBE are congruent, and ∠CBD and ∠DBE are congruent, we can conclude that ∠ABD and ∠DBE are also congruent. (Angles opposite to congruent angles are congruent)
5. We know that the sum of the measures of ∠ABD and ∠DBE is 180 degrees because ∠ABC and ∠CBD are supplementary angles.
6. Since ∠ABD and ∠DBE are congruent and their sum is 180 degrees, each angle must measure 90 degrees.
7. Therefore, the angle between the bisectors AD and CE is a right angle.

Conclusion:
The angle between the bisectors of two adjacent supplementary angles is always a right angle. Therefore, the correct answer is option B) Right angle.

If angle of adjacent supplementary angle is 180 degree. given:now bisection of this angle. So then formed 1/2×180 90 It means that it is the right angle.