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°

Answer 1

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. To determine which set of angles from the provided options is valid, we can add the angles in each option and check if they equal 180 degrees.

1. Option 1: 59°, 58°, and 63°

   • Sum: 59 + 58 + 63 = 180°

2. Option 2: 59°, 63°, and 48°

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

3. Option 3: 57°, 54°, and 69°

   • Sum: 57 + 54 + 69 = 180°

4. Option 4: 54°, 44°, and 82°

   • Sum: 54 + 44 + 82 = 180°

The angle measures in options 1, 3, and 4 all sum to 180 degrees, while option 2 does not. The valid angle measurements are from options 1, 3, and 4.

So, the valid responses that follow the Triangle Angle Sum Theorem are:

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

If you need only one measure, just refer to any of the options listed above.