Complementary and Supplementary Angles

These two angles are complementary. Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary.                                                                                

These two angles can be "pasted" together to form a right angle!                         

These two angles are supplementary. Supplementary Angles Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary.                                                                       

These two angles can be "pasted" together to form a straight line!                                                 

Complementary and Supplementary Find the missing angle. 1. Two angles are complementary. One measures 65 degrees. 2. Two angles are supplementary. One measures 140 degrees. Answer : 25 Answer : 40

Complementary and Supplementary Find the missing angle. You do not have a protractor. Use the clues in the pictures. 2. 1. x x 55 165 X=35 X=15

Interior and Exterior Angles of Triangles

Sums of Interior Angles Triangle Quadrilateral Pentagon = 2 triangles = 3 triangles Hexagon Octagon = 4 triangles Heptagon = 5 triangles = 6 triangles

Convex Polygon # of Sides # of Triangles Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 3 1 180 4 2 360 5 3 540 6 4 720 7 5 900 8 6 1080 n n – 2 180•(n – 2)

Interior Angles 1 2 3 4 5 6 Exterior Angles

Sums of Exterior Angles 1 2 3 4 5 6 180 180 180•3 = 540 180 Sum of Interior & Exterior Angles = 540 Sum of Interior Angles = 180 Sum of Exterior Angles = 540- 180= 360

Sums of Exterior Angles Polygon # of Sides Interior + Exterior Interior Angles Exterior Angles Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 540 180 360 720 360 360 900 540 360 1080 720 360 Sum of Exterior Angles is always 360!

Angles of Regular Polygons Sum of the Interior Angles 180(n – 2) Sum of the Exterior Angles Always 360! 180(n – 2) Each Interior Angle n Each Exterior Angle 360 n

Parallel Lines And Transversals

Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n

Vertical Angles & Linear Pair Two angles that are opposite angles. Vertical angles are congruent.  1   4,  2   3,  5   8,  6   7 Supplementary angles that form a line (sum = 180) 1 & 2 , 2 & 4 , 4 &3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8

Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. Corresponding angles Alternate interior angles Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. Consecutive interior angles Consecutive exterior angles Continued…..

Corresponding Angles & Consecutive Angles Corresponding Angles: Two angles that occupy corresponding positions.  2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8

Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8

Alternate Angles  3   6,  4   5  2   7,  1   8 1 2 3 4 5 6 Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.  3   6,  4   5  2   7,  1   8 1 2 3 4 5 6 7 8

Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80°

If line AB is parallel to line CD and s is parallel to t, find: Example: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A ANSWERS: 1. 30 2. 35 3. 33