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Finding Measures of Angles and Arcs in Tangent Circles

This guide focuses on finding the measures of angles and arcs when a line is tangent to a circle. We will explore examples that illustrate how to determine the angles formed at the points of tangency and their corresponding arc measures. Solutions to guided practice problems are provided for clarity, offering step-by-step explanations for better understanding. This comprehensive approach will reinforce concepts related to tangent lines, angles, and the properties of circles, ensuring learners can apply these principles effectively.

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Finding Measures of Angles and Arcs in Tangent Circles

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  1. = a. m1 12 (130o) (125o) 2 = b. m KJL EXAMPLE 1 Find angle and arc measures Line mis tangent to the circle. Find the measure of the red angle or arc. SOLUTION = 65o = 250o

  2. = m1 12 (210o) for Example 1 GUIDED PRACTICE Find the indicated measure. SOLUTION = 105o

  3. m TSR (98o) 2 = for Example 1 GUIDED PRACTICE Find the indicated measure. SOLUTION = 196o

  4. m XY (80o) 2 = for Example 1 GUIDED PRACTICE Find the indicated measure. SOLUTION = 160o

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