Download Missing Measurement Problems: -Linear Pairs/supplementary

Honors Geometry 6-1 Notes
Missing Measurement Problems:
-Linear Pairs/supplementary angles
-int. angles of triangles = 180˚
-isos. triangles: base angles are congruent
-sum of remote interior angles = the ext.
angle of a triangle.
-vertical angles are congruent
-parallel line "stuff"
-comp. angles
-The sum of the angles around a common
vertex is 360˚
Honors Geometry 6-1 Notes
Honors Geometry 6-1 Notes
Polygon Sum Formula:
The Sum of the measures of all
n interior angles of an n-gon is:
What if the polygon is equiangular or regular?
Then Formula for one Angle
is:
Honors Geometry 6-1 Notes
Examples
64
114
102 135
Honors Geometry 6-1 Notes
w = _______
Note: This nonagon is regular.
x = _______
y = _______
w
z = _______
Note:
y is
linear
with z
x
y
z
z = 40˚ + 40˚
Honors Geometry 6-1 Notes
b
a
c
e
d
What is a + b + c + d + e ?
Honors Geometry 6-1 Notes
b
a
e
c
d
Honors Geometry 6-1 Notes
e
a
d c
b
Honors Geometry 6-1 Notes
a
e
b
d c
Honors Geometry 6-1 Notes
This is the Exterior Angle Sum
Formula: For any polygon the sum of the
measures of a set of exterior angles is:
Set?
Exactly 1 exterior angle per vertex
Honors Geometry 6-1 Notes
If our polygon is equiangular or regular
then:
Each exterior angle is:
Each interior angle is:
Honors Geometry 6-1 Notes
Examples:
1. What is the measure of one exterior angle
in a regular pentagon?
because each
ext. angle
would be 30˚
2. If I know the interior angle of a regular
polygon is 150 degrees. How many sides
does the polygon have?
Honors Geometry 6-1 Notes
Missing Measurement:
-Linear Pairs/supplementary angles
-triangles = 180˚
-isos. triangles: base angles are equal
-remote interior angles = the ext. angle of
a triangle.
-vertical angles are congruent
-parallel line "stuff"
-comp. angles
-The sum of the angles around a common
vertex is 360˚
NOW: Know SUM of interior and exterior
angles of any polygon.
Honors Geometry 6-1 Notes
6-1: 12-41
Finish Proofs by Next Tuesday
(Purple Day) or Next Wednesday
(White Day)