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