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

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

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

Let’s Practice…

Let’s Practice…

Let’s Practice…

Let’s Practice…

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

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

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

Let’s Practice…

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

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

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.