Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.

Question

(1 point)
Responses

46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees

42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees

50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees

46°, 49°, and 85°

Answer 1

To find the measures of each angle in a triangle using the Triangle Angle Sum Theorem, we recall that the sum of the angles in a triangle is always 180 degrees.

To determine which set of angles adds up to 180 degrees, let's analyze each response:

1. 46°, 50°, and 85°:

   • Sum: 46 + 50 + 85 = 181° (not valid)

2. 42°, 44°, and 79°:

   • Sum: 42 + 44 + 79 = 165° (not valid)

3. 50°, 54°, and 93°:

   • Sum: 50 + 54 + 93 = 197° (not valid)

4. 46°, 49°, and 85°:

   • Sum: 46 + 49 + 85 = 180° (valid)

Thus, the only valid set of angles that adds up to 180 degrees is 46°, 49°, and 85°.