1. Inscribed Angle
Definition: An inscribed angle has its vertex on the circle and its sides are chords.
Picture:

2. Inscribed Angle Conjecture
Conjecture: The measure of an angle inscribed in a circle is half the measure of the intercepted arc. Example:
Inscribed (Angle A)
Central (Angle B)
Arc 50
100 80
160 40

3. Let’s Practice If angle A is 50, what is angle B?
If angle B is 80, what is angle A?

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8. Inscribed Angles Intercepting the Same Arc
Conjecture: Inscribed angles that intercept the same are congruent. Picture: ∠𝐶𝐴𝐵 𝑖𝑠 𝑐𝑜𝑛𝑔𝑢𝑟𝑒𝑛𝑡 𝑡𝑜 ∠𝐶𝐷𝐵

9. Let’s Practice
If angle PAQ is 40 degrees, what is angle PBQ?

10. Angles Inscribed in a Semi-Circle Conjecture
Conjecture: Angles inscribed in a semi-circle are right angles. Picture:

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12. Parallel Lines Intercepted Arcs Conjecture
Conjecture: The distance between two parallel lines that intercept a circle is the same. Picture:

13. Let’s Practice…
What is the measure of C?

14. Let’s Practice…
A regular pentagon is inscribed in a circle. Find the measure of 𝑃𝐸 .
72…Angle P is 108, then subtract from 180.