Angles of Triangles Lesson #2 Pg. 19

Key Vocabulary Triangle Interior Angle Exterior Angle A figure formed by three line segments that intersect only at their endpoints Interior Angle An angle inside a polygon Exterior Angle The angle formed by one side of a triangle and the extension of the adjacent side Remote Interior Angles The angles of a triangle that are not adjacent to a given exterior angle

Real World Link What is true about the measures of and ? What kind of angle is formed by , & ? Write an equation representing the 3 angles Lines m and n are parallel, Lines p and r are transversals A m 1 3 5 n 2 4 B C p r

Sum of the Angles in a Triangle The sum of the measures of the Interior angles of any triangle is 180°. Geometers Sketchpad x + y + z = 180° y° z° x°

Example Find the value of x in the Antigua and Barbuda flag. x° 55°

Example In , if 72° and 74°, what is the ? Draw a Diagram…

Example The measures of the angles of are in a ratio of 1:4:5, what are the measures of the angles? Draw a diagram….

Example The measures of the angles of are in a ratio of 2:4:6, what are the measures of the angles? Draw a diagram….

Image Definition (Exterior and Interior Angles) One interior angle and the exterior angle that share the adjacent side are a “Linear Pair” (180°) Interior Exterior

Exterior Angles of a Triangle Interior Exterior The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles (NOT ADJACENT)

Exterior Angles of a Triangle The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles A 1 B C

Example Suppose . Find the measure of . K 2 1 4 L 5 M

Homework HC: pg. 23-24 (1-15) REG: pg. 23-24 (1-7, 9, 11, 14, 15)