Question
Several students made comments about this image.
A triangle has angles B, C, D. The exterior angle to angle B is A.
Which comment is true?
“If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other two angles.”
“If I know the measure of C, I can find the measure of angle A because they are the same.”
“If I know the measures of angles C and B, I can find the measures of A and D.”
“If I know the measure of angle A, I can find the measure of angle D by subtracting from 180.”
A triangle has angles B, C, D. The exterior angle to angle B is A.
Which comment is true?
“If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other two angles.”
“If I know the measure of C, I can find the measure of angle A because they are the same.”
“If I know the measures of angles C and B, I can find the measures of A and D.”
“If I know the measure of angle A, I can find the measure of angle D by subtracting from 180.”
Answers
GPT-4o mini
Let's analyze each comment in relation to the properties of triangles and exterior angles.
1. **“If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other two angles.”**
- This statement is **false**. While angle A and angle B can be used in calculations, you cannot simply subtract both from 180 to find angles C and D. The correct approach is that angle A is equal to the sum of angles C and D (due to the exterior angle theorem), and you would need more information to find these angles individually.
2. **“If I know the measure of C, I can find the measure of angle A because they are the same.”**
- This statement is **false**. Angle A is an exterior angle corresponding to angle B, and is equal to the sum of angles C and D, not equal to angle C itself.
3. **“If I know the measures of angles C and B, I can find the measures of A and D.”**
- This statement is **true**. If you know angles C and B, you can find angle A using the exterior angle theorem (A = B + C) and then find angle D since the sum of angles in a triangle is 180 degrees (D = 180 - (B + C)).
4. **“If I know the measure of angle A, I can find the measure of angle D by subtracting from 180.”**
- This statement is **false**. Knowing angle A does not directly allow you to find angle D just by subtracting from 180 degrees. You would first need to find angle B (which would be A = B + C) and angle D would relate to B and C, not directly derived from A alone.
Based on this analysis, the only true comment is: **“If I know the measures of angles C and B, I can find the measures of A and D.”**
1. **“If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other two angles.”**
- This statement is **false**. While angle A and angle B can be used in calculations, you cannot simply subtract both from 180 to find angles C and D. The correct approach is that angle A is equal to the sum of angles C and D (due to the exterior angle theorem), and you would need more information to find these angles individually.
2. **“If I know the measure of C, I can find the measure of angle A because they are the same.”**
- This statement is **false**. Angle A is an exterior angle corresponding to angle B, and is equal to the sum of angles C and D, not equal to angle C itself.
3. **“If I know the measures of angles C and B, I can find the measures of A and D.”**
- This statement is **true**. If you know angles C and B, you can find angle A using the exterior angle theorem (A = B + C) and then find angle D since the sum of angles in a triangle is 180 degrees (D = 180 - (B + C)).
4. **“If I know the measure of angle A, I can find the measure of angle D by subtracting from 180.”**
- This statement is **false**. Knowing angle A does not directly allow you to find angle D just by subtracting from 180 degrees. You would first need to find angle B (which would be A = B + C) and angle D would relate to B and C, not directly derived from A alone.
Based on this analysis, the only true comment is: **“If I know the measures of angles C and B, I can find the measures of A and D.”**