These activity sheets will teach your students how to correctly measure angles outside a circle.

If you have a circle you can determine measure of the angle formed by two secants, tangents or a secant and a tangent from a point outside the circle using the outside angle theorem. The measure of that angle will be half of difference of the values of the intercepted arcs. We can use this for all sorts of rays. Scientists often use this theorem to understand the angle at which the sun light/heat rays touch Earth. If you think about it, the sun and the rays it gives off are just a circle and two tangent rays coming off of it.

These worksheets explain how find the measure of an angle outside of a circle. Your students will use these worksheets to learn how to measure angles outside a circle, whether formed by tangents, secants, etc.

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Print Angles in a Circle Worksheets

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Angles Outside a Circle Lesson

This worksheet explains how to find the measure of an angle outside of a circle. A sample problem is solved, and two practice problems are provided.

Outside Worksheet

Students will study each drawing and calculate the measure of an angle outside of a circle. Ten problems are provided.

Skill Practice

Use the skills that you work on here to determine the value of the measures outside of the circle.

Review and Practice

We look at how to use a reference angle to determine all the other measures that work off of that single known angle.

Skill Quiz

Students will demonstrate their proficiency with using this skill in a set format. Ten problems are provided.

Angles Outside a Circle Skills Check

Students will find the measure of angles outside of circles. Three word problems are provided, and space is included for students to copy the correct answer when given.

How do you find the measures of angles inside and outside circles?

An angle is considered inside a circle when its vertex is present inside the circle, and its lines lie on two cords of a circle. The term for such an angle is "inscribed angle." The measure of an inscribed angle is computed as half that of the arc that the two sides of the angle cut out from the circle. An angle that is outside a circle is one that has a vertex that is outside the circle, and its sides are secants or tangents. This category of angles has three types: 1) An angle formed by one tangent. 2) An angle formed by two tangents. 3) An angle formed by two secants. Similar to an angle that is inside a circle or on it, an angle outside a circle has a particular formula that involves intercepted arcs. Such an angle is known as an "exterior angle." It has its vertex where two rays share an endpoint outside a circle. Those two rays are the sides of the angle. The measure of an exterior angle is computed by dividing the difference between the measures of the intercepted arcs by 2.