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![Geometry Worksheets for School and Home](https://static.wixstatic.com/media/49609e_4375edf449221b9ec0654010a69c6864.png/v1/fill/w_80,h_80,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/49609e_4375edf449221b9ec0654010a69c6864.png)
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Geometry for School and Home
![Geometry worksheet in which students apply a theorem to calculate the measures of angles in the exterior of a circle from the measures of their intercepted arcs.](https://static.wixstatic.com/media/49609e_616286a658624176b2c35f2605989e72.jpg/v1/fill/w_404,h_553,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/49609e_616286a658624176b2c35f2605989e72.jpg)
![Geometry worksheet in which students apply a theorem relating the measures of angles in the exterior of a circle and the measures of their intercepted arcs to calculate measures of angles and arcs.](https://static.wixstatic.com/media/49609e_5c431a9e53734706b3885141ffa087ba.jpg/v1/fill/w_424,h_524,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/49609e_5c431a9e53734706b3885141ffa087ba.jpg)
Activity 3.8
Assignment 3.9
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Assignment 10.13
Angles in the Exterior of a Circle and Arc Measures
Objective
Develop and apply theorems relating angles in the exterior of circles and their intercepted arcs.
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About Geometry Worksheet Assignment 10.13:
Assignment 10.13 is an introduction to the theorem about the measures of angles with a vertex at the intersection of secants or tangents in the exterior of a circle and the measures of their intercepted arcs.
Prerequisite Skills: Identify arcs intercepted by lines intersecting a circle (Assignment 10.10). Solve algebraic equations with one variable.
Theorem: The measure of an angle with vertex at the intersection of secants or tangents in the exterior of a circle is one-half the difference of the measures
of the arcs intercepted by the angles.
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