Problem #DES-anglescircles

Descriptions
 10–14

Problem

Certain geometric objects nicely blend when they happen to be together in a problem, one possible example of such a pair of objects is a circle and an inscribed angle.
We will be using the following statements in the examples and problems:
1. The supplementary angles (angles "hugging" a straight line) add up to \(180^{\circ}\).
2. The sum of all internal angles of a triangle is also \(180^{\circ}\).

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3. Two triangles are pronounced "congruent" if ALL their corresponding sides and angles are equal.
We recommend solving the problems in this sheet in the order of appearance, as some problems use statements from previous problems as a step in the solution. Specifically, problem 6.2’s statement is required to solve every other problem that comes after it.