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11.1 Angle Measures in Polygons
Unit IIIH Day 1
Do Now
• What is the sum of the measures of the interior
angles of a triangle?
• … a quadrilateral?
Measures of Interior and Exterior Angles
Polygon
Triangle
# of
sides
3
# of
triangles
1
Quadrilateral
Pentagon
Hexagon
…
Nonagon (9)
n-gon
n
Sum of measures of
interior ’s
1●180=180
2●180=360
Polygon Interior Angles Theorem
• The sum of the measures of the interior angles of a
convex n-gon is _________
• COROLLARY: The measure of each interior angle of a
regular n-gon is _________
Ex. 1: Finding measures of Interior
Angles of Polygons
• Find the value of x in the diagram shown:
Ex. 2: Finding the Number of Sides
of a Polygon
• The measure of each interior angle is 140. How
many sides does the polygon have?
Exterior Angles
• Exterior angles
Thm. 11.2: Polygon Exterior Angles
Theorem
• The sum of the measures of the exterior angles
of a convex polygon (one angle at each vertex) is
________
• COROLLARY: The measure of each exterior
angle of a regular polygon is _________
Ex. 3: Finding the Measure of an
Exterior Angle
• Find the value of x.
Ex. 3: Finding the Measure of an
Exterior Angle
• Find the value of x.
Ex. 4: Angle measures of a polygon
• A home plate marker for a softball field is a
pentagon. Three of the interior angles of the
pentagon are right angles. The remaining two
interior angles are congruent.
• What is the measure of each angle?
Ex. 5: Using Angle Measures of a
Regular Polygon (real life)
• If you were designing the home plate marker for
some new type of ball game, would it be possible
to make a home plate marker that is a regular
polygon with each interior angle having a
measure of 135°? What about 145°?
Closure
• Explain in words how to find the measure of
each interior angle and each exterior angle in a
regular polygon.