1. 10.4 Inscribed Angles and Polygons

2. What We will Learn
Use inscribed angles
Use inscribed polygons

3. Needed Vocab
Inscribed angle: angle whose vertex is on a circle and whose sides contain chords
Intercepted arc: arc that lies between two lines, rays, or segments
Inscribed polygon: when all vertices lie on a circle
Circumscribed circle: circle that contains the vertices of the polygon

4. Ex. 1 Using Inscribed Angles
Measure of an inscribed angle is one-half the measure of its intercepted arc
Find the indicated measure
A. 𝑚∠𝑇
24°
B. arc QR
80°

5. Ex. 2 Finding Measure of Intercepted Arc
Find arc RS and 𝑚∠𝑆𝑇𝑅.
Arc RS
62°
𝑚∠𝑆𝑇𝑅
31°

6. Ex. 3 Finding Angle Measure
Given 𝑚∠𝐸=75°, find 𝑚∠𝐹.
75°

7. Ex. 4 Using Inscribed Polygons
Find each value
2𝑥=90
2𝑥 2 = 90 2
𝑥=45°
B. find y and z degrees
Remember that opposite angles of an inscribe polygon are supplementary. Y: 60 Z:
100