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

Answer 1

Interpretation: the triangle's interior angles are C, A, and 33°. The exterior at the 33° vertex is D, the exterior at A is B, and the exterior at C is 128°. Thus interior C = 180 − 128 = 52°. Then A = 180 − (52 + 33) = 95°. So D = 180 − 33 = 147° and B = 180 − 95 = 85°.

Evaluate statements:

- B = C + 33: 85 = 52 + 33 → True.
- B = 180 − (D + 128): 85 = 180 − (147 + 128) = −95 → False.
- B = 360 − (D + 128): 85 = 360 − (147 + 128) = 85 → True.
- D + B + 128 = 360: 147 + 85 + 128 = 360 → True.
- 180 = D + B + 128 = 360: false (D + B + 128 = 360, not 180) → False.
- D = 360 − 33: 147 ≠ 327 → False.
- D = 180 − 33: 147 = 147 → True.
- B = D + 128: 85 ≠ 275 → False.

So the true statements are: 1, 3, 4, and 7.