Section 4 2 Notes Angles of Triangles EQ

Section 4. 2 Notes: Angles of Triangles EQ: How are the angle measures of triangles related?

Triangle Angle Sum Theorem The sum of the measures of the angles of a triangle is 180

Example 1: SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle.

Exterior Angle One side of the triangle and the extension of an adjacent angle ∠ 4 is the exterior of ∆ABC Remote Interior Angles Each exterior angle of a triangle has two remote interior angles that are not adjacent to the exterior angles ∠ 1 & ∠ 3 are the remote interior angles of ∆ABC Exterior Angles Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. m∠ 1 + m∠ 3 = m∠ 4

Example 2: • ∠O and ∠W are remote interior angles Therefore : m∠O + m∠W = m∠L x + 32 = 2 x - 48 Solve for x : x = 80

A theorem with a proof that follows as a direct result of another theorem Corollary The acute angles of a right triangle are complementary B Corollary to the Triangle Sum Theorem 4. 1 ∠A + ∠B = 90° C A There can be at most one right or obtuse angle in a triangle L Corollary to the Triangle Sum Theorem 4. 2 J K If ∠L is obtuse, then ∠J & ∠K are acute

Example 3: • 48° + 56° = 104° 180° - 104° = 76° 90° - 48° = 42° 180° - 132° = 48°

Example 4: Find m 3 if m 5 = 130 and m 4 = 70.

Example 4: Find m 1 if m 5 = 142 and m 4 = 65.

Example 4: Find m 2 if m 3 = 125 and m 4 = 23.

Got It Find each measure. 1. m∠ 1 2. m∠ 2 3. m∠ 3