Lesson 4-2: Angles of Triangles

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Presentation transcript:

Lesson 4-2: Angles of Triangles TARGETS Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem. Target

LESSON 4-2: Angles of Triangles Tri angle sum th

Use the Triangle Angle-Sum Theorem LESSON 4-2: Angles of Triangles EXAMPLE 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. WORK REASONS Triangle Angle-Sum Th. Vertical angles 1  2 m1 = m2 63 = m2 Def of Congruent Substitution Triangle Angle-Sum Th. Check The sums of the measures of the angles in each triangle should be 180. m1 + 43 + 74 = 63 + 43 + 74 or 180 m2 + m3 + 79 = 63 + 38 + 79 or 180 Ex1: Tri Ang Sum Th

LESSON 4-2: Angles of Triangles Ex Angle The

Answer: So, mFLW = 2(80) – 48 or 112. LESSON 4-2: Angles of Triangles EXAMPLE 2 Use the Exterior Angle Theorem GARDENING Find the measure of FLW in the fenced flower garden shown. WORK REASONS mLOW + mOWL = mFLW Exterior Angle Theorem x + 32 = 2x – 48 Substitution 32 = x – 48 80 = x Answer: So, mFLW = 2(80) – 48 or 112. Ex2 Ext Ang Th.

LESSON 4-2: Angles of Triangles EXAMPLE 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle. WORK REASONS Exterior Angle Theorem m1 = 48 + 56 m1 = 104 Linear Pair Substitution 104 + m2 = 180 76 m 3 + 48 = 90 m 3 = 42 Complementary Ex3 Right Tri

Find the measure of each numbered angle. LESSON 4-2: Angles of Triangles EXAMPLE 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle. WORK REASONS (90 – 34) + m2 + m 4 = 180 Triangle Sum Theorem Substitution 56 + 76 + m 4 = 180 132 + m4 = 180 m4 = 48 Triangle Angle-Sum Theorem m5 + 41 + 90 = 180 m5 + 143 = 180 m5 = 49 Ex3 Right Tri