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

Question

(1 point)
Responses

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

54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees

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

59°, 63°, and 48°

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees. To find the correct measures of the angles among the options provided, we can calculate the total for each set of angles listed:

1. 59°, 58°, and 63°

   • \(59 + 58 + 63 = 180°\) (Valid)

2. 54°, 44°, and 82°

   • \(54 + 44 + 82 = 180°\) (Valid)

3. 57°, 54°, and 69°

   • \(57 + 54 + 69 = 180°\) (Valid)

4. 59°, 63°, and 48°

   • \(59 + 63 + 48 = 170°\) (Not valid)

The three valid combinations that meet the Triangle Angle Sum Theorem are:

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

However, without more context or specific angle measurements from the diagram, we cannot determine which is the correct set of angles for the triangle in question. Please check the diagram to see which angles or measurements correspond to the triangle, and select the appropriate response.