Question

Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.

(1 point)
Responses

57°
57
°
, 54°
54
°
, and 69°
69
°
57 degrees , 54 degrees , and 69 degrees

59°
59
°
, 58°
58
°
, and 63°
63
°
59 degrees , 58 degrees , and 63 degrees

59°
59
°
, 63°
63
°
, and 48°
48
°
59 degrees , 63 degrees , and 48 degrees

54°
54
°
, 44°
44
°
, and 82
answer

Answer 1

To find the measures of the angles in a triangle using the Triangle Angle Sum Theorem, we need to remember that the sum of the interior angles of a triangle is always 180 degrees.

If you are given one angle, you can find the sum of the other two angles by subtracting the known angle from 180 degrees.

However, without a specific angle provided in the question or a diagram to reference, we will evaluate the provided options based on the angle sum rule.

1. **57°, 54°, and 69°**:
- Sum = 57 + 54 + 69 = 180°

2. **59°, 58°, and 63°**:
- Sum = 59 + 58 + 63 = 180°

3. **59°, 63°, and 48°**:
- Sum = 59 + 63 + 48 = 170° (not a valid triangle)

4. **54°, 44°, and 82°**:
- Sum = 54 + 44 + 82 = 180°

Based on the Triangle Angle Sum Theorem, the valid sets of angles that form a triangle are:

- **57°, 54°, and 69°**
- **59°, 58°, and 63°**
- **54°, 44°, and 82°**

The angles 59°, 63°, and 48° do not sum to 180°, so they are not valid. Thus the angles in the first, second, and fourth responses are valid for a triangle.

If you can provide more context or the specific angles given in the problem, I’d be able to assist further!