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Angle A has a measure of 45°. Angle B is made from 36 one-degree angles. Which sentence is true?

A. The measure of angle A is 9° greater than the measure of angle B.
B. The measure of angle B is 9° greater than the measure of angle A.
C. The measure of angle A is 81° greater than the measure of angle B.
D. The measure of angle B is 81° greater than the measure of angle A.

Sagot :

GinnyAnsweridn
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."
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