Triangles

The three angles must add to 180o

Exterior Angles

Variables

55o

X+74 54o

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.

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)

Angles with the same measure are congruent.

If m1 = m2, then 1 2

Congruent

“curtains”

Vertical Angles

• Vertical angles are two nonadjacent angles formed by two intersecting lines

• Vertical angles are ALWAYS congruent

12

34

Angles 1 and 3 are vertical;Angles 2 and 4 are vertical.

Complementary Angles

• Complementary angles are 2 angles whose measures have a sum of 90 degrees

• Complementary angles can be adjacent or nonadjacent

200

700

Supplementary Angles

• Supplementary angles are 2 angles whose measures have a sum of 180 degrees.

• Supplementary angles can be adjacent or nonadjacent.

520 1280

Angles

• “small” angles are equal

• “big” angles are equal

• One big and one small equal 180