11.2 Angle Theorems for Triangles What can you conclude about the measures of the angles of a triangle? The sum of the measures of the interior angles of a triangle is always 180°. The measure of an exterior angle is equal to the sum of its remote interior angles.

180-5x 180-5x 5x Review

11x° + 4x° = 180° => 15x° = 180° => x =12 BCF = 4(12) AND CFE = 11(12) 4x° 11x° Review

Plug X into Missing Angles 7x°+40° + 3x° = 180° 10x + 40 = 180 10x = 140 x = 14 Plug X into Missing Angles CFG => 3(14) = 42° DCF => 180-42 = 138° Review

Justifying Triangle Sum Theorem States that for triangle ABC, m<A + m<B + m<C = 180 ° Justifying Triangle Sum Theorem You can use your knowledge of parallel lines intersected by a transversal, to informally justify the triangle sum theorem. Pg. 354 in textbook What angle is alt. int. angle to 4 and 5? What would be the degrees if you added angles 1, 2 and 3? 180°

How many degrees are in a triangle? 180° 63 +42 + x = 180 Example

Identifying the theorem of a triangle Identify the vertices (corners of triangle) Add measures of angles to equal 180° 29 + 61+ x = 180 90 + x = 180 -90 -90 71 + 56 + x = 180 X = 90 127 + x = 180 90° -127 -127 X = 53° Identifying the theorem of a triangle

Vocabulary Interior angle – formed by two sides of the triangle. Exterior angle – formed by one side of the triangle and the extension of an adjacent angle; Exterior Angle, when extended, will form a 180° angle. Remote interior angle – interior angle that is not adjacent to the exterior angle. Vocabulary

180° Since we extended the line and created angle 4, the extension created a ___________ angle. 180°

9x+4+4x+1+97=180 13x +102 = 180 13x = 78 => x=6 Example To find C: Subtract 180-83 = 97 <A = 9x +4 <B = 4x + 1 <C = 97 A + b + c = 180 9x+4+4x+1+97=180 13x +102 = 180 13x = 78 => x=6 Example

5y+3+4y+8+34 = 180 9y+45=180 9y=135 => y=15 180 -146 34 M = 5(15) + 3; M=78 N = 4(15) + 8; N = 68 78 + 68 + 34 = 180

CW – pg. 358 # 1-7 HW – 11.2 HRW CW and HW