Download Finding Angle Measures in Polygons SUM of INTERIOR angles = (n 2)

Geometry
Notes – 8.2
Name_________________________
Finding Angle Measures in Polygons
diagonal –
2
3
SUM of INTERIOR angles =
1
(n  2) 180
triangle =
4
6
quadrilateral =
5
n=6
Examples 1 – 2:
1. Find the sum of the measures of the interior angles of a convex octagon.
2. The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by
the number of sides.
Practice 3 – 4:
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
R
SUM of the EXTERIOR angles =
Examples 6 – 7:
89
6. What is the value of x in the diagram?
67
2x
x
7. 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?
interior angle + exterior angle =
Examples 8 – 9:
8. Find the measures of an interior angle and an exterior angle of a regular pentagon.
9. Each interior angle of a regular n-gon has a measure of 168°. Find the number of sides.
Practice 10 – 11:
10. Find the measures of an interior angle and an exterior angle of a regular dodecagon.
11. Each interior angle of a regular n-gon has a measure of 157.5°. Find the number of sides.