Question
Which statements are true for the image below? Check all that apply.
A triangle has angles C, A, 33 degrees. The exterior angle to angle with measure of 33 degrees is D, the exterior angle to A is B, the exterior angle to angle C is 128 degrees.
Measure of angle B = measure of angle C + 33 degrees
Measure of angle B = 180 degrees minus (measure of angle D + 128 degrees)
Measure of angle B = 360 degrees minus (measure of angle D + 128 degrees)
Measure of angle D + measure of angle B + 128 degrees = 360 degrees
180 degrees = measure of angle D + measure of angle B + 128 degrees = 360 degrees
Measure of angle D = 360 degrees minus 33 degrees
Measure of angle D = 180 degrees minus 33 degrees
Measure of angle B = measure of angle D + 128 degrees
A triangle has angles C, A, 33 degrees. The exterior angle to angle with measure of 33 degrees is D, the exterior angle to A is B, the exterior angle to angle C is 128 degrees.
Measure of angle B = measure of angle C + 33 degrees
Measure of angle B = 180 degrees minus (measure of angle D + 128 degrees)
Measure of angle B = 360 degrees minus (measure of angle D + 128 degrees)
Measure of angle D + measure of angle B + 128 degrees = 360 degrees
180 degrees = measure of angle D + measure of angle B + 128 degrees = 360 degrees
Measure of angle D = 360 degrees minus 33 degrees
Measure of angle D = 180 degrees minus 33 degrees
Measure of angle B = measure of angle D + 128 degrees
Answers
Answered by
GPT-4o mini
To determine which statements about the angles in the triangle are true, let's analyze the relationships between the angles based on geometric principles.
1. **Exterior Angles Theorem**: The exterior angle (D) of a triangle is equal to the sum of the two opposite interior angles. Thus, for angle D at angle C (which is 33 degrees), we have:
\[
D = A + 33°
\]
2. **Angle Relationships**: The relationship for angle B (the exterior angle to angle A) can be described as follows:
\[
B = C + A
\]
Since C is given as 33 degrees, we have:
\[
B = A + 33°
\]
3. **Sum of Angles in Triangle**: The angles in a triangle add up to 180 degrees:
\[
A + B + C = 180°
\]
Given this understanding, let's evaluate each statement:
1. **Measure of angle B = measure of angle C + 33 degrees**: This implies \( B = C + 33° \). Since C = 33°, \( B = 33° + 33° = 66° \), which does not follow the exterior angle rule. Therefore, **False**.
2. **Measure of angle B = 180 degrees minus (measure of D + 128 degrees)**: This is not correct based on our exterior angles. **False**.
3. **Measure of angle B = 360 degrees minus (measure of D + 128 degrees)**: This is also incorrect. **False**.
4. **Measure of angle D + measure of angle B + 128 degrees = 360 degrees**: This does not hold based on previous analysis. **False**.
5. **180 degrees = measure of angle D + measure of angle B + 128 degrees = 360 degrees**: This is incorrect based on the definition of angles in relation to a triangle. **False**.
6. **Measure of angle D = 360 degrees minus 33 degrees**: This provides an incorrect calculation of angle D. **False**.
7. **Measure of angle D = 180 degrees minus 33 degrees**: This yields another incorrect calculation for angle D. **False**.
8. **Measure of angle B = measure of angle D + 128 degrees**: This is not consistent with our understanding based on exterior angle properties. **False**.
With the given analysis, all statements are **False** based on geometrical relationships involving triangles and exterior angles. Please check the conditions or rephrase the angles for more accurate verification.
1. **Exterior Angles Theorem**: The exterior angle (D) of a triangle is equal to the sum of the two opposite interior angles. Thus, for angle D at angle C (which is 33 degrees), we have:
\[
D = A + 33°
\]
2. **Angle Relationships**: The relationship for angle B (the exterior angle to angle A) can be described as follows:
\[
B = C + A
\]
Since C is given as 33 degrees, we have:
\[
B = A + 33°
\]
3. **Sum of Angles in Triangle**: The angles in a triangle add up to 180 degrees:
\[
A + B + C = 180°
\]
Given this understanding, let's evaluate each statement:
1. **Measure of angle B = measure of angle C + 33 degrees**: This implies \( B = C + 33° \). Since C = 33°, \( B = 33° + 33° = 66° \), which does not follow the exterior angle rule. Therefore, **False**.
2. **Measure of angle B = 180 degrees minus (measure of D + 128 degrees)**: This is not correct based on our exterior angles. **False**.
3. **Measure of angle B = 360 degrees minus (measure of D + 128 degrees)**: This is also incorrect. **False**.
4. **Measure of angle D + measure of angle B + 128 degrees = 360 degrees**: This does not hold based on previous analysis. **False**.
5. **180 degrees = measure of angle D + measure of angle B + 128 degrees = 360 degrees**: This is incorrect based on the definition of angles in relation to a triangle. **False**.
6. **Measure of angle D = 360 degrees minus 33 degrees**: This provides an incorrect calculation of angle D. **False**.
7. **Measure of angle D = 180 degrees minus 33 degrees**: This yields another incorrect calculation for angle D. **False**.
8. **Measure of angle B = measure of angle D + 128 degrees**: This is not consistent with our understanding based on exterior angle properties. **False**.
With the given analysis, all statements are **False** based on geometrical relationships involving triangles and exterior angles. Please check the conditions or rephrase the angles for more accurate verification.