To determine which sentence is true, let’s first identify the measures of angles A and B.
1. Measure of Angle A:
- Given directly as [tex]\(45^\circ\)[/tex].
2. Measure of Angle B:
- Described as being made from 36 one-degree angles.
- Therefore, the measure of Angle B is [tex]\(36^\circ\)[/tex].
Next, we will compare the measures of Angle A and Angle B to see which statement is true from the given options.
Option A: The measure of angle A is 9° greater than the measure of angle B.
- Calculate the difference: [tex]\(45^\circ - 36^\circ = 9^\circ\)[/tex].
- This is true because [tex]\(45^\circ\)[/tex] (Angle A) is indeed 9° greater than [tex]\(36^\circ\)[/tex] (Angle B).
Option B: The measure of angle B is 9° greater than the measure of angle A.
- Calculate the difference: [tex]\(36^\circ - 45^\circ = -9^\circ\)[/tex].
- This is false because Angle B is not greater than Angle A; in fact, it is 9° less.
Option C: The measure of angle A is 81° greater than the measure of angle B.
- Calculate the difference: [tex]\(45^\circ - 36^\circ = 9^\circ\)[/tex].
- This is false because the difference is not 81°; it is only 9°.
Option D: The measure of angle B is 81° greater than the measure of angle A.
- Calculate the difference: [tex]\(36^\circ - 45^\circ = -9^\circ\)[/tex].
- This is false because the difference is not 81°, and Angle B is not greater than Angle A.
Based on the above comparisons, the correct sentence is option A:
"The measure of angle A is 9° greater than the measure of angle B."
