Download Geometry - Shelbyville CUSD #4

Geometry
Section 3-5
Angle of a Polygon
Polygon- A plane figure that meets the following conditions:
1.
It is formed by three or more segments called sides, such that no
two sides with a common endpoint are collinear.
2.
Each side intersects exactly two other sides, one at each
endpoint (it’s enclosed).
Convex Polygon- A polygon that has no line that contains a side of the
polygon and also contains a point in the interior of the polygon.
Concave (or Nonconvex Polygon- A polygon that is not convex. It has
a whole.
State whether the following figures are polygons. If the figure is a
polygon, state whether it is convex or concave.
Polygons are named by the number of sides.
3 – Triangle
6 – Hexagon
9 – Nonagon
n – n-gon
4 – Quadrilateral
7 – Heptagon
10 – Decagon
5 – Pentagon
8 – Octagon
12 – Dodecagon
Regular Polygon- A polygon that is equilateral and equiangular. Name
some regular polygons.
State whether the polygon is regular.
Diagonal- A segment that joins two nonconsecutive vertices of a
polygon.
What is the sum of the measures of the angles in a triangle? A
quadrilateral? A pentagon? A hexagon? An n-gon?
The sum of the measures of the interior angles of a convex n-gon is
(n-2)180.
(n  2) 180
The measure of each interior angle of a regular n-gon is
.
n
Examples:
1.
Find the value of x in the diagram shown.
2.
The measure of each interior angle of a regular polygon is 165o.
How many sides does the polygon have?
3.
A heptagon has four interior angles that measure 160o each and
two interior angles that are right angles. What is the measure of
the other interior angle?
4.
Find the measure of each angle in a regular 11-gon.
The sum of the measures of the exterior angles of a convex polygon, one
angle at each vertex, is 360o.
0
The measure of each exterior angle of a regular n-gon is 360 .
n
5.
Find the value of the variable in each diagram.
a.
b.
6.
The measure of each exterior angle of a regular polygon is 40o.
How many sides does the polygon have?
7.
The sign on a building has a long narrow hexagon shape. Four
of the interior angles measure 140o each. The remaining two
interior angles at each end of the sign are congruent. What is
the measure of each angle?
8.
If you were designing a sign for a new building, would it be
possible to make a sign that is a regular polygon with each angle
having a measure of 160o? 115o?
Classroom Exercises: p. 103 HW: p. 104-105 2-18 even, 22a