Geometry of Triangles and Angles

In triangles BDC and CEB, both have a 90-degree angle (at D and E), share the base BC, and have equal base angles (angle C = angle B) because triangle ABC is isosceles. By AA similarity, BDC ~ CEB.

Sony Cybershot cameras featured a 270-degree wide angle lens in several models, allowing for versatile shooting angles including selfies and creative perspectives. The 300, 330, and 360 degree options are not standard specifications for Cybershot cameras. 270-degree tilting screens were a key feature distinguishing Cybershot in the compact camera market.

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.

The Great Pyramid of Giza has an inclination angle of approximately 51 degrees and 51 minutes. This precise angle was carefully calculated by ancient Egyptian architects to achieve structural stability and visual harmony. The slope represents the ratio of height to base length.

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.