answer each question as indicated. what is the sum measures of the interior angles of a triangle?...
TRANSCRIPT
Answer each question as indicated.
What is the sum measures of the interior angles of a triangle?
Answer: 180
Answer each question as indicated.
What is the measure of each angle of an equilateral triangle?
Answer: 60
Answer each question as indicated.
What is the sum measures of the interior angles of a quadrilateral?
Answer: 360
Determine the sum of the measures of the interior and exterior angles of the triangle.
Determine the sum of the measures of the interior and exterior angles of a quadrilateral.
Make generalizations on the sum of the measures of the interior and exterior angles of a polygon.
EXERCISES• TELL WHETHER OR NOT EACH
OF THE FOLLOWING IS A POLYGON.
Exercises • TELL WHETHER A POLYGON IS
CONVEX OR NOT.
POLYGONS POLYGONS and its partsand its partsPOLYGONS POLYGONS
and its partsand its partsReview Review
POLYGON PARTS
POLYGON PARTS
Side - one of the line segments that make
up the polygon.
Vertex - point where
two sides meet. Two or
more of these points
are called vertices.
POLYGON PARTS Diagonal -
a line connecting
two vertices
that isn't a side.
ANGLE SUM MEASURES
Angle Sum measure of the interior angles of a polygon
Polygon No. of sides No. of non-overlapping diagonals
No. of Trianglesformed
Angle Sum measure
triangle 3 0 1 1 x 180°or 180°
Quadrilateral 4 1 2 2 x 180°or 360°
Pentagon 5 2 3 3 x 180°or 540°
N- gon n n-3 n-2 (n-2)180°
Examples:
1. What is the sum of the measures of the interior angles of a convex polygon with
a. 11 sides b. 15 sides
Solutions:a. Sa = (n – 2) 180⁰
= (11 – 2) 180⁰
= 9(180⁰) = 1620⁰
Examples:
1. What is the sum of the measures of the interior angles of a convex polygon with
a. 11 sides b. 15 sides
Solutions:b. Sa = (n – 2) 180 ⁰
= (15 – 2) 180⁰ = 13(180⁰) = 2340⁰
Examples:
2. Find the sum of the measures of the interior angles of a convex heptagon.
Solutions:b. Sa = (n – 2) 180⁰
= (7 – 2) 180 ⁰ = 5(180 ⁰) S = 900⁰
Examples:
3. How many sides does a convex polygon have if the sum of the measures of its interior angles is 1440 ?⁰
Solutions:b. Sa = (n – 2) 180⁰ 1440⁰ = (n – 2) 180⁰ 1440 = 180⁰ n – 360⁰
n =
n =
n = 10
180
3601440
180
1800The polygon has 10 sides.
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES
OF THE VERTEX ANGLES IS GIVEN
4. 1260°
S=(n-2)180
1260 =180n-360
1260+360= 180n
1620 = 180n
n= 9
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES
OF THE VERTEX ANGLES IS GIVEN
4. 1260°
n =(S180) + 2
= (1260 180) + 2
= 7 + 2
n= 9
QUIZ
A. FIND THE SUM OF THE MEASURES OF THE VERTEX
ANGLES FOR EACH POLYGON
1.15-gon
2.50- gon
3.35-gon
B. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN
1.1260°
2.1620°
Angle Sum Measures of the Exterior Angles of a Polygon
LESSON 7
POLYGON PARTS Interior Angle - Angle
formed by two adjacent sides inside the polygon.
Exterior Angle - Angle
formed by two adjacent sides outside the polygon.
Investigate
1, 2 and 3 are interior angles.
4,5 and 6 are exterior angles
1 + 4 = 180° 2 + 5 = 180° 3 + 6 = 180°
112
3
4
5
6
If m1= 70, what is the measure 4?
m4= 110 If m2 = 80, what is the
m5? m5= 100 If m3 = 30, what is the
m6? m6= 150
112
3
4
5
6
The sum of the exterior angles of an n-gon is 360°
m4= 110m5= 100m6= 150
m2 + m4 + m6=360 112
3
4
5
6
160°
70°
120°120°
70°
60°
110°
20°
60°
110°
60° + 60 ° + 110 ° + 20 ° + 110° = 360°
Angle Sum measure of the exterior angles of a polygon
Polygon No. of sides
Angle Sum
measure (interior angles)
Measure of EACH INTERIOR angle of a regular
n-gon
Angle Sum
measure (exterior angles)
Measure of EACH exterior angle of a regular
n-gon
triangle 3 1 x 180°or 180°
180°3
360° 360°3
Quadrilateral
4 2 x 180°or 360°
360°4
360° 360°4
Pentagon 5 3 x 180°or 540°
540°5
360° 360°5
N- gon n (n-2)180° (n-2)180°n
360° 360°n
Examples:
1. How many degrees are there in each of the exterior angle of a regular hexagon?
Solution:Ea =
Ea =
= 60
n
360
6
360
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE
MEASURE OF THE EXTERIOR ANGL E IS GIVEN
1.30°
2.10°
QUIZQUIZQUIZQUIZ
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE
VERTEX ANGLES IS GIVEN
1.1980°
2.4320°
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE
MEASURE OF THE EXTERIOR ANGLE IS GIVEN
1.24°
2.45°