1. Triangles The three angles must add to 180 o

3. Exterior Angles

4. Variables 55 o X+74 54 o

5. Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is (n - 2) 180. A decagon has 10 sides, so n = 10. Sum = (n – 2)(180) Polygon Angle-Sum Theorem = (10 – 2)(180) Substitute 10 for n. = 8 180 Simplify. = 1440 Find the sum of the measures of the angles of a decagon.

6. Polygon Angle-Sum Theorem The sum of the measures of the angles of a given polygon is 720. How can you use the Polygon Angle-Sum Theorem to find the number of sides in the polygon? Sum = (n – 2) 180 Write the Equation 720 = (n – 2) 180 Sub. In known values 720 = 180n – 360 Simplify 1080 = 180n Addition Prop of EQ 6 = n Hexagon (6 sides)

7. Angles with the same measure are congruent. If m  1 = m  2, then  1   2 Congruent “ curtains ”

8. Vertical Angles Vertical angles are two nonadjacent angles formed by two intersecting lines Vertical angles are ALWAYS congruent 1 2 3 4 Angles 1 and 3 are vertical; Angles 2 and 4 are vertical.

9. Complementary Angles Complementary angles are 2 angles whose measures have a sum of 90 degrees Complementary angles can be adjacent or nonadjacent 20 0 70 0

10. Supplementary Angles Supplementary angles are 2 angles whose measures have a sum of 180 degrees. Supplementary angles can be adjacent or nonadjacent. 52 0 128 0

11. Angles “small” angles are equal “big” angles are equal One big and one small equal 180