Lesson 4 2 Angles of Triangles TARGETS Apply

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

LESSON 4 -2: Angles of Triangles

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. 1 2 Vertical angles 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

LESSON 4 -2: Angles of Triangles

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 = 2 x – 48 Substitution 32 = x – 48 80 = x Answer: So, m FLW = 2(80) – 48 or 112.

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

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