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Triangle Perimeter and Angle Calculations in Geometric Problems

This document presents a series of warm-up exercises focused on finding the perimeter of a triangle given the lengths of its sides, as well as solving various angle-related problems involving circles and arcs. The exercises include calculating unknown sides and angles based on provided data while enhancing understanding of geometric properties, such as the relationship between angles and arcs in circles. This resource is ideal for students studying geometry and seeking practice in applying mathematical concepts.

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Triangle Perimeter and Angle Calculations in Geometric Problems

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  1. Warm-up A 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P 3. MCY = 270 Find BC. B 2. Find ACB 20 B A M 312 20 90 B 24 C C Y

  2. Case III:Vertex is outside the circle C ANGLE small ARC A D LARGE ARC B LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  3. Ex. 6 Find m1. 1 15° A D 65° m<1 = 25 degrees B

  4. Ex. 7 Find mAB. mAB = 16 degrees A 27° 70° B

  5. Ex. 8 Find m1. 260° 1 m<1 = 80 degrees

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