1. 8.3 Inscribed Polygons
There are a couple very helpful Theorems about Polygons Inscribed within circles that we will look at

2. Semicircle Theorem An angle inscribed in a semicircle is a right angle
∟D = ∟C = ∟E = ∟F = 90° F E

3. Example 1: Given: Angle A = 25° and AB is the diameter Find: Angle B
Solution 1:
AB is the diameter so ΔABC is a right triangle
∟C = 90° semicircle theorem
∟A + ∟B + ∟C = 180° angles of a triangle
25° + ∟B + 90° = 180° substitution
∟B = 180° - 90° - 25° algebra
∟B = 65° C A B

4. Inscribed Quadrilateral Theorem
The opposite angles of an inscribed quadrilateral add up to 180°
∟A + ∟D = 180°
∟B + ∟C = 180° A B C D

5. Example 1: Given ∟C = 100° Find ∟A and ∟B Given ∟D = 60°
Solution 1:
∟A and ∟C are opposite
∟B and ∟D are opposite
∟A + ∟C = 180° → ∟A and ∟100° = 180°
∟A = 80°
∟B + ∟D = 180° → ∟B and ∟60° = 180°
∟B = 120° B A C D