In Euclidean geometry, the sum of interior angles of any triangle equals two right angles.

• A. One right angle
• B. Two right angles
• C. Three right angles
• D. Zero right angles

Answer: (B)

The key idea is that in the flat, Euclidean plane the interior angles of any triangle add up to a straight angle: 180 degrees, which is two right angles. A common way to see this is to draw a line through one vertex that is parallel to the opposite side. The two interior angles at the other two vertices become corresponding (alternate interior) angles with angles along that parallel line, so together with the angle at the chosen vertex they fill a straight line. That makes the total 180 degrees, i.e., two right angles.

This property holds for every triangle in the plane, regardless of shape. In other geometries, the sum changes: in hyperbolic geometry the sum is less than 180 degrees, and in spherical geometry it’s greater than 180 degrees.

Why not the other options? A sum of only one right angle would be 90 degrees, which isn't enough to close a triangle in the plane. Three right angles amount to 270 degrees, which is too much for a triangle, and zero right angles would give 0 degrees, which isn’t possible for a polygon’s interior angles.