Download Geometry – Warm Up Quadrilaterals Day 1 Classifying Polygons

Name_________________________
Geometry – Warm Up Quadrilaterals Day 1
1. If the measures of two angles of a triangle are 19° and 80°, find the measure of the third angle.
2. Solve (x – 2)180 = 1980
3. Find the value of x.
4. What does it mean if a polygon is
- equilateral?
- equiangular?
54°
x°
Today we will learn about polygons
At the end of today, you will be able to classify polygons and find interior and exterior
angles of polygons.
Classifying Polygons
A ____________________ is a closed plane figure with the following properties:
– it is formed by three or more segments called sides
– each side intersects with exactly two sides, one at each endpoint
convex
concave
Classifying Polygons
Number of sides
3
4
5
6
7
8
9
10
12
n
Type of Polygon
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
dodecagon
n-gon
Vocabulary
Equilateral –
Equiangular –
Regular –
Example 1
Sketch an example of a convex heptagon. Then sketch an example of a concave heptagon.
Finding Angle Measures in Polygons
diagonal –
2
3
Theorem –
The sum of the measures of the interior angles
of a convex n-gon is (n − 2)  180°.
1
4
6
Corollary –
The sum of the measures of the interior angles of a quadrilateral is 360°.
Examples
1. Find the sum of the measures of the interior angles of a convex octagon.
5
n=6
2. The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon
by the number of sides.
3. A coin is in the shape of a regular 11-gon. Find the sum of the measures of the interior angles.
4. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon
by the number of sides.
Q
5. Use the diagram to find ∠ S and ∠ T.
156°
P 93°
85°
T
S
6. The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the
measure of the fourth interior angle.
R
Theorem –
The sum of the measure of the EXTERIOR angles of a convex polygon is ALWAYS 360°.
7. What is the value of x in the diagram?
89°
67°
2x°
x°
8. A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the
measure of an exterior angle at the sixth vertex?
9. Find the measures of an interior angle and an exterior angle of a regular pentagon.
10. Each interior angle of a regular n-gon has a measure of 168°. Find the value of n.