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When we talk about geometry, we're referring to the branch of mathematics that deals with the shapes, sizes, positions and properties of space. It encompasses various figures, from simple lines and curves to more complex forms like polygons and polyhedra. A fundamental part of geometry is studying angles, which is the measure of the turn that separates two intersecting lines or line segments.

In the context of the given problem, understanding geometry helps us comprehend how angles interact with each other, specifically when discussing complementary angles, which play a core role in the formation of right angles. These concepts are crucial in fields that range from architectural design to robotics and from art to astronomy, showcasing the vast applications of geometry.

Diving into the complement of an angle, this term signifies an important relationship between two angles whose measures add up to a right angle, that is, a total of 90 degrees. Given any angle measure, its complement is simply calculated by subtracting it from 90 degrees.

It's pertinent to note that the complement only exists for acute angles, those measuring less than 90 degrees, since an obtuse angle (greater than 90 degrees) would not meet the criteria of creating a right angle with any positive measure angle. When we seek the complement of an angle, we are essentially seeking that missing piece to complete a right angle, which is a foundational concept in geometry for constructing squares, rectangles, and even understanding the workings of triangles.

Moving on to right angles, these are angles that exactly measure 90 degrees and they are omnipresent in our everyday life. A right angle is what you see in the corner of a book, the edges of a door, or a street intersection that crosses at a perfect perpendicular layout.

In geometry, right angles are special because they are used as a benchmark to define other angles. For instance, angles smaller than a right angle are called acute angles, and those larger are called obtuse angles. Right angles are fundamental in determining perpendicularity and they hold major importance in constructing and analyzing shapes that are central to both practical and theoretical geometry.