Geometry of Triangles and Angles

The interior angles of any planar triangle always add up to 180 degrees. This is a fundamental theorem of Euclidean geometry.

An isosceles triangle has at least two equal angles (and consequently two equal sides). This triangle has angles 110°, 30°, and 40° - all three are different, making it a scalene triangle, not isosceles.

An oblique angle is any angle that is not a multiple of 90° (not 0°, 90°, 180°, 270°, etc.). Angles greater than 180° are called reflex angles, not oblique angles. The statement incorrectly identifies the term.

A right angle is exactly 90 degrees, which is one-quarter of a full 360-degree rotation. It's the angle formed when two lines are perpendicular to each other. 45° is half of a right angle, 180° is a straight line, and 360° is a complete rotation.

A right angle measures exactly 90 degrees, like the corner of a square. 45° is half a right angle, 180° is a straight angle, and 360° is a full rotation.

All four statements are true. A: Triangle interior angles sum to 180° (fundamental property). B: Triangle inequality theorem - any two sides sum exceeds the third. C: Exterior angles (one per vertex) sum to 360°. D: Exterior angle theorem - exterior angle equals sum of remote interior angles.

An equilateral triangle must have three 60-degree angles. A right triangle must have one 90-degree angle. Since a triangle cannot have both a 90-degree and three 60-degree angles, a right triangle can never be equilateral.

In a general triangle, the centroid (intersection of medians) and the incenter (intersection of angle bisectors) are different points. They only coincide in an equilateral triangle. Therefore, the statement is false.

Supplementary angles are defined as two angles whose measures sum to 180°, not 90°. Angles that sum to 90° are called complementary angles. Therefore, the statement 'Two angles are supplementary if they sum to 90 degrees' is false. The correct answer is False.

The orthocenter of a triangle is the intersection point of its three altitudes. In an obtuse triangle, the altitudes from the acute vertices lie outside the triangle, and their intersection point (the orthocenter) is indeed located outside the triangle. This is a well-known geometric property. The statement is true.

An equilateral triangle has three equal sides. If it shares two sides with a parallelogram, those two adjacent sides of the parallelogram must be equal to the sides of the triangle, and thus equal to each other. A parallelogram with equal adjacent sides is a rhombus. Thus, the statement is true.

In an isosceles triangle, the base is the side of unequal length, while the two legs are the equal sides. By the triangle inequality theorem, any side of a triangle must be less than the sum of the other two sides. Therefore, the base cannot be greater than the sum of the two legs - it must be less than their sum. The statement is false, and the correct answer is False.

By definition in geometry, two angles are complementary if the sum of their measures is exactly 90 degrees. Therefore, the statement is true.

The sum of the interior angles of a square is always 360 degrees (90 degrees * 4), not 180 degrees. Therefore, this statement is incorrect, making it the correct option.