Geometry
1.6 Polygon Angle Measures
Name: _____________________________
Directions: Fill in the following blanks below using the words in the box below!
REGULAR POLYGON
EQUIANGULAR
EQUILATERAL
CONCAVE
CONVEX
DIAGONAL
HEXAGON
POLYGON
OCTAGON
VERTEX
1. A closed plane figure formed by three or more sides is called a ________________________.
2. A polygon in which all sides are equal or congruent is called _____________________________.
3. A segment that joins two non-adjacent vertices in a polygon is called a ______________________.
4. A polygon in which all vertices point outward is called _______________________.
5. A polygon in which at least one vertex points inward is called _______________________.
6. A convex polygon that has all congruent sides and angles is called a ______________________.
7. A polygon in which all of the interior angles are equal or congruent is called ________________________.
8. A polygon that has six sides is called a(n) ________________________.
9. A polygon that has eight sides is called a(n) __________________________.
10. A point where two sides of a polygon meet is called a _________________.
Match each vocabulary term on the left with a part of polygon ABCDE on the right.
11. a diagonal
12. a side of the polygon
13. a vertex of the polygon
_________
_________
_________
A. point D
B. CE
C. CD
Tell whether each figure is a polygon. If it is a polygon, name it by the number of sides.
14.
15.
16.
Tell whether each polygon is regular or irregular. Then tell whether it is concave or convex.
17.
18.
19.
8.1 Angle Measures in Polygons
Goal: Find the measure of the interior angles in a polygon.
 n- gon- a polygon with ______ sides and ______ vertices
 Consecutive Vertices- _______ vertices that are endpoints of the ________________ side.
 Diagonal (of a polygon)- A segment that joins two ___________________________ vertices.
Polygon Interior Angles Theorem (Theorem 8.1)
The sum of the measures of the interior angles of a convex n- gon is: _______________________
𝑚∠1 + 𝑚∠2 + 𝑚∠3 + ⋯ + 𝑚∠𝑛 = _______________________________
 The sum of the measures of the interior angles of a quadrilateral is _______________
Ex. Find the sum of the measures of the interior angles of a convex octagon
Using the sum to find # of sides (n)
Ex. The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the
number of sides.
Ex. Find the value of 𝑥 in the diagram.
𝐴
108°
𝐷
*This polygon is a _____________________
𝐵
𝑥°
121°
59°
𝐶
Find the value of 𝒙 of a pentagon whose angles have measures of:
5𝑥°, 139°, 9𝑥°, 71°, 92°.
A pentagon has an interior angle sum of: ______________
Polygon Exterior Angles Theorem (Theorem 8.2)
The sum of the measures of the exterior angles of a
convex polygon, one angle at each vertex, is __________
3
2
4
𝑚∠1 + 𝑚∠2 + 𝑚∠3 + ⋯ + 𝑚∠𝑛 = ___________
1
5
*The value of n (# sides) does not influence the sum!!
Ex. Find the value of 𝒙.
(𝑥 + 20)°
𝑥°
96°
112°
Ex. Find the measures of an interior angle and an exterior angle of a regular 12- gon.
(*Remember: Regular means the sides and angles are congruent!)
Ex. Each interior angle of a regular n-gon has measure of 156°. Find the value of n.