Download Interior / Exterior Angles in Polygons

Interior / Exterior Angles in Polygons
1. An exterior angle is an angle that forms a linear pair with one of the interior angles of a polygon.
Sketch an exterior angle at each vertex
2. Exterior angle theorem in triangles – any exterior angle of a triangle is equal in measure to the sum
of the two remote interior angles.
1 is an exterior
 2 and 3 are the remote interiors
m1 = m2 + m3
Examples)
mC = 42o and mB = 105o. Find mCAD.
If mC = x + 12, mB = 2x – 27, and
mCAD = 4x+30. Find mC, mB,
and mCAB .
Find mACB
3. Naming Polygons:
4. Now – how many triangles can each polygon be divided into?
5.
Sum of the interior angles of a polygon:
(n – 2) x 180o , where n is the number of sides
6.
One Interior Angle of a regular polygon:
(n – 2) x 180o / n
ex) What is the sum of
the measures of the
interior angles of a
hexagon?
ex) What is the measure of
one interior angle of a
regular hexagon?
(remember – regular means all angles and sides congruent!)
7.
Sum of the of the exterior angles of a polygon
360o
8.
One Exterior Angle of a regular polygon
360o / n
ex) what is the measure of one
exterior angle of a 12 sided polygon?
What is the measure of one interior angle?
ex) what is the sum of the
measures of the exterior
angles of a hexagon?
ex) what is the measure
of one exterior angle
of a regular hexagon?
ex) the sum of the interior angles of
a polygon is 540o. How many sides
does it have?
Practice with Interior and Exterior Angles
For #1 – 3 , find the sum of the interior angles and the sum of the exterior angles.
1. 5 sided polygon
2. 10 sided polygon
3. 12 sided polygon
For #4 - 6, find the measure of each angle specified in the regular polygons shown.
4.
5.
xo
yo
xo
yo
6. Each interior angle of a regular
polygon measures 102o. How many
sides does the polygon have?
7. The measure of one exterior angle of a
regular polygon equals 18o. How many sides
does the polygon have?
8. Find the the value of x
9. Find the value of x
(x-13)o xo
(x+12)
157o
o
98o
10. Find the value of x.
(x-34)o
122o
138o
11. If mA = 70o and mB = 60o, find
mACD and mACB.
12. If mA = 40o and mACD = 120o,
find mACB and mB.
14. In the Following diagram, mBAD = 16x + 5
mACB = 5x +5, mABC = 3x + 16.
Find mACB, mCBA, and mBAC.
13.
If mA = 40o, mB = 3x + 20, and
mACD = 5x + 10, find mB,
and mACD.
15. In the diagram shown below,
mABD=42°, mBDC=77°. What is
mBAD? What is mDCB?
16. Challenge: Find the measures of the following angles:ACB, ECF, CFE, CED,
DCE, and ACD. The order the angles are listed is not necessarily the order you need to work in!