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Measuring MeasuringAngles AnglesininRadians Radians 12-3-EXT 12-3-EXT Lesson Presentation HoltMcDougal GeometryGeometry Holt 12-3-EXT Measuring Angles in Radians Objectives Use proportions to convert angle measures from degrees to radians. Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians Vocabulary radian Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians One unit of measurement for angles is degrees, which are based on a fraction of a circle. Another unit is called a radian, which is based on the relationship of the radius and arc length of a central angle in a circle. Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians If a central angle θ in a circle of radius r intercepts an arc of length r, the measure of θ is defined as 1 radian. Since the circumference of a circle of radius r is 2πr, an angle representing one complete rotation measures 2π radians, or 360°. 2π radians = 360° and π radians = 180° π radians 1° = 180° 180° and 1 radian = π radians Use these facts to convert between radians and degrees. Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians Example 1: Converting Degrees to Radians Convert each measure from degrees to radians. A. 85° 17 85° π radians 180° 36 = 17 π 36 π radians 180° 2 = A. 90° 1 90° Holt McDougal Geometry π 2 12-3-EXT Measuring Angles in Radians Example 2: Converting Radians to Degrees Convert each measure from radians to degrees. A. 1 2π 3 2 π radians 3 60 Π 180° radians = 120° 180° radians = 30° π 6 B. 1 π radians 6 Holt McDougal Geometry 30 Π