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

Question

Responses:
59°, 58°, and 63°
59°, 63°, and 48°
57°, 54°, and 69°
54°, 44°, and 82°
choose one answer.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.

From your options, we can check the sums:

1. 59°, 58°, and 63°

   • Sum: 59 + 58 + 63 = 180° (valid)

2. 59°, 63°, and 48°

   • Sum: 59 + 63 + 48 = 170° (not valid)

3. 57°, 54°, and 69°

   • Sum: 57 + 54 + 69 = 180° (valid)

4. 54°, 44°, and 82°

   • Sum: 54 + 44 + 82 = 180° (valid)

Based on this, the valid sets of angles that satisfy the Triangle Angle Sum Theorem are:

• 59°, 58°, and 63°
• 57°, 54°, and 69°
• 54°, 44°, and 82°

Since you are looking for a single choice, without further context on a specific triangle, I will present the candidates without favoring one.

However, if you require only one option to choose, you can select any of the three valid sets. If there is a specific angle or triangle context that needs to be considered, please clarify!