Which set of angle measures could be the measures of the interior angles of a triangle?

Question

50°, 60°, and 75°
35°, 105°, and 45°
62°, 62°, and 62°
90°, 45°, and 45°

Answer 1

To determine which set of angle measures could represent the interior angles of a triangle, we need to remember that the sum of the interior angles of a triangle is always 180 degrees.

Let's check each set:

1. 50°, 60°, and 75°

   • Sum = 50 + 60 + 75 = 185° (not a triangle)

2. 35°, 105°, and 45°

   • Sum = 35 + 105 + 45 = 185° (not a triangle)

3. 62°, 62°, and 62°

   • Sum = 62 + 62 + 62 = 186° (not a triangle)

4. 90°, 45°, and 45°

   • Sum = 90 + 45 + 45 = 180° (this is valid for a triangle)

The only set of angle measures that could represent the interior angles of a triangle is 90°, 45°, and 45°.