Download Chapter 8.1 Notes: Find Angle Measures in Polygons

Chapter 8.1 Notes: Find Angle
Measures in Polygons
Goal: You will find interior and exterior angle
measures in polygons.
Properties of a Polygon
• In a polygon, two vertices that are endpoints of the
same side are called consecutive vertices.
• A diagonal of a polygon is a segment that joins two
nonconsecutive vertices.
Finding Interior Angle Measures in Polygons
• Theorem 8.1 Polygon Interior Angles Theorem:
The sum of the measures of the interior angles of a
convex n-gon is (n – 2)180.
• Corollary to Theorem 8.1 Interior Angles of a
Quadrilateral:
The sum of the measures of the interior angles of a
quadrilateral is 360o.
Ex.1: Find the sum of the measures of the interior
angles of a convex octagon.
GUIDED PRACTICE
for Examples 1 and 2
1. The coin shown is in the
shape of a regular 11- gon.
Find the sum of the measures
of the interior angles.
ANSWER 1620°
2. The sum of the measures of the interior angles of
a convex polygon is 1440°. Classify the polygon
by the number of sides.
ANSWER
decagon
Ex.2: The sum of the measures of the interior angles of
a convex polygon is 900o. Classify the polygon by
the number of sides.
Ex.3: Find the value of x in the diagram shown.
Ex.4: In the diagram below, find mS and
mT .
Ex.5: The sum of the measures of the interior angles of
a convex polygon is 1440o. Classify the polygon by
the number of sides.
Finding Exterior Angle Measures in Polygons
• Theorem 8.2 Polygon Exterior Angles Theorem:
The sum of the measures of the exterior angles of a
convex polygon, one angle at each vertex, is 360o.
Exterior Angle Sum Theorem
Exterior Angle Sum Theorem
If a polygon is convex, then the
sum of the measures of the
exterior angles, one at each
vertex, is 360°.
Ex.6: What is the value of x in the diagram shown?
Ex.7: A convex hexagon has exterior angles with
measures 34o, 49o, 58o, 67o, and 75o. What is the
measure of an exterior angle at the sixth vertex?
Ex.8: The trampoline shown is shaped like a regular
dodecagon. Find (a) the measure of each interior
angle, and (b) the measure of each exterior angle.
Ex.9: A stop sign is shaped like a regular octagon.
Find (a) the measure of each interior angle, and (b )
the measure of each exterior angle.