Download Discovering Geometry Day 35

Discovering Geometry
Day 35
5.1 Polygon Sum Conjecture
o Daily Openers
o Check homework
5.1 Polygon Sum Conjecture
 Create a chart with the number of sides of a polygon and the sum of the measures of the
interior angles.
 Do you notice a pattern?
 Find a model (formula) that gives the angle sum for any polygon given the number of sides.
# of sides of polygon
Sum of the angle
measures
3
4
5
6
7
8
…
n
180
?
?
?
?
?
…
?
Conjecture – the sum of the measures of the interior angles of a
polygon is:
(n-2) · 180
where n is the number of sides of the polygon.
Ex. Find the sum of the interior angles of a dodecagon.
Ex. Find the sum of the interior angles of a 25-gon.
Ex. Find the missing angle in each:
Conjecture – the measure of each interior angle of an equiangular
polygon is found by:
n  2 180
n
where n is the number of sides
6.2 Exterior Angles of a Polygon
# of sides of polygon
3
4
5
6
7
8
…
n
Sum of measures of exterior
angles
360
?
?
?
?
?
…
?
conjecture – the sum of the measures of a set of exterior angles is 360.
conjecture – the measure of each angle of a regular polygon can be found
by using the formula:
180 
360
n
Homework – pages 259–260 #1–14, 16
Daily Openers – 1. Are the ’s ?
If so, why?
2. Are the ’s ?
If so, why?
3. Find the area of an equilateral  with a side length of 18 cm.
4. An isosceles  has base angles that measure: 2x + 17˚ and 5x + 3˚.
Find the measure of each angle.
5. What is the measure of the vertex angle in #4.