Download YOU TRY - WordPress.com

Name: ______________________________________
Date:________________
Unit 5 Geometry: Relationships in Triangles and Quadrilaterals (Red)
Section 5.7
Find Angle Measures in Polygons
Page 298 - 303
Essential Question: How do you find angle measures in polygons?
Vocabulary:
 A _______________________ of a polygon is a segment that joins two nonconsecutive vertices.

______________ _______________ _____________ Theorem states that the sum of the measures
of the interior angles of a convex n-gon is _________ • 180°.

_________________ _______________ of a ______________________ Theorem states that the
sum of the measures of the interior angles of a quadrilateral is 360°.

______________________ _________________ ________________ Theorem states that the sum
of the exterior angles of a convex polygon, one angle at each vertex is 360°.

When the sides of a polygon are extended, other angles are formed. The original angles are the
_______________ _______________ of the polygon. The angles that are adjacent to the interior
angles are the ____________ ______________ of the polygon. In a ________________ polygon,
the interior angles are congruent.
EXAMPLE 1: Find the sum of angle measures in a polygon
Find the sum of the measures of the interior angles of a convex hexagon.
A hexagon has _____ sides. Use the Polygon Interior Angles Theorem.
(n - 2) ∙ 180° = ( _____ - 2 ) ∙ 180°
= (
) ∙ 180°
= ________°
is the sum of the INTERIOR measures of a hexagon.
EXAMPLE 2: Find the number of sides of a polygon
The sum of the measures of the interior angles of a convex polygon is 2700°. Classify the polygon by the
number of the sides.
Using the Polygon Interior Angles Theorem to write an equation involving “n” sides. Then solve.
(n - ___) ∙ _______° = ______°
Polygon Interior Angle Theorem
YOU TRY:
n – 2 = ______
Divide each side by 180°
n = _______
This polygon has ______ sides. It is a _____-gon.
Name: ______________________________________
Date:________________
YOU TRY:
1.
Find the sum of the measures of the interior angles of the polygon to the right.
2.
The sum of the measures of the interior angles of a convex polygon is 540°. Classify the polygon by
the number of sides.
EXAMPLE 3: Find an unknown interior angle measure
Find the value of x in the diagram
The polygon is a ________________. Use the Corollary to the Polygon Interior
angles Theorem to write an equation involving x. Then solve.
x° + ______ + _______ + _______ = _________
x
= _________
EXAMPLE 4: Find an unknown exterior angle measure
Find the value of x in the diagram to the right.
Use the Polygon Exterior Angles Theorem to write an equation involving x.
Then solve for x.
x° + ______ + _______ + _______ + ________ = _________
x
= _______________
YOU TRY:
3.
What is the value of x in the diagram to the right?
4.
A convex heptagon has exterior angles with measures 60°, 51°, 67°, 48°, 32°, and 59°. What is the
measure of an exterior angle at the seventh vertex?