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Warm up
x
1.
30°
2.
3.
4.
y
x=
85°
y=
65°
115°
If <A in a triangle equals 70° what is the combined measure of <B and <C?
110°
If ΔXYZ has three congruent angles, what is the measure of <X?
60°
Find the measure of each angle.
x=5
(2x2 + 5)
(3x2 + 2x + 10)
(8x - 10)
30°, 55°, 95°
Number of sides
n
Number of Δ
regions
Sum of measures
of interior angles
3
1
180°
4
2
360°
5
3
540°
6
4
(Number of sides 1. Copy this table
720°
2 ) times 180° = sum of interior angles
2. Fill in the first column
3. Just using one vertex, draw as many diagonals as you can in each shape.
4. Fill in the middle column
5. How many degrees in a triangle?
6. Fill in the last column.
7. Look at this:
The measure of
INTERIOR ANGLES
in a polygon
In a polygon with n sides, the total
measure of interior angles =
180(n – 2)
The measure of
EXTERIOR ANGLES
in a polygon
is always 360°
Example:
This is a
REGULAR
pentagon.
Find the measures of each interior
and each exterior angle in the
pentagon.
You can start by finding the interior
OR the exterior measures.
Find the INTERIOR measure first:
180(5-2) =
180(3) =
540° (total interior degrees)
540/5 = 108°
Therefore the exterior is 72°
Find the EXTERIOR measure first:
360/5 = 72°
Therefore the interior is 108°
Try this one
Draw a regular octagon
♥ Find the sum of
the measures of
the interior
♥1080°
angles.
♥ Find the
measure of
EACH interior
♥135°
angle.
♥ Find the
measure of
EACH exterior
angle.
♥45°
Another practice problem…
Find the sum of the
measures of the exterior
angles in an 11-gon.
360°
IF the 11-gon was regular,
what would be the measure
of EACH exterior angle?
≈32.73°
What would be the
measure of EACH interior
angle?
≈147.27°
The fish problem
(put this in your notes)
115°
120°
y°
54°
x°
z°
48°
100°
X = 78°
Y = 102°
Z = 127°
Uno mas
Find the measure of
an interior angle
and an exterior
angle in a regular
dodecagon
Exterior
360/12 = 30°
Interior
180° – 30° = 150°
Assignment
Pg 180, 9-40