Question

Which interior angles are possible for a triangle? The measures of the interior angles of a triangle are 90°, 40°, and 50°. The measures of the interior angles of a triangle are 82°,38°, and 60°. The measures of the interior angles of a triangle are 65°, 25°, and 75°. The measures of the interior angles of a triangle are 57°, 70°, and 33°. The measures of the interior angles of a triangle are 59°, 31°, and 90

Answer 1

The sum of interior angles of a triangle is always* 180°, so the following triangles are possible:

• 90°, 40°, 50°
• 82°, 38°, 60°
• 59°, 31°, 90°

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The following are not possible triangles.

• 65°, 25°, 75° — add to 165° ≠ 180°
• 57°, 70°, 33° — add to 160° ≠ 180°

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* in plane Euclidean geometry. There are other topologies such that the sum of angles of a triangle differs from 180°.