Download Triangle Sum Rule The sum of the measures of the angles in a

Chapter 8 Lesson 4
Triangle Sum Rule
The sum of the measures of the angles in a
triangle is 180˚
m∠1 + m∠2 + m∠3 = 180˚
The small letter "m" in front of ∠1 says
"the measure of angle 1" (m∠1)
To find the sum of angle measures in any 4-sided
figure you can divide the figure in two by drawing a
diagonal.
A diagonal is a line segment that connects two nonadjacent vertices of a polygon.
The diagonal creates two
triangles. Since the sum of each
triangle is 180˚ the sum of the four
sided figure is 2•180˚= 360˚
Sum of the angle of a quadrilateral
The sum of the measures of the angles
in a quadrilateral is 360˚
m∠1 + m∠2 + m∠3 +m∠4 = 360˚
Examples:
1. Find the unknown angle measures in the
triangle.
2. Find the unknown angle measure in the
quadrilateral.
In a convex polygon, all diagonals can be
drawn within the interior of the figure. When
you divide any convex polygon into triangles
you can find the sum of its interior angle
measures.
5 triangles so...
5•180˚= 900˚
Diagonals:
When we figure out the sum of the angles we only
want to use diagonals to make triangles.
We can really draw more diagonals than that.
diagonals for sum of angles
total number of diagonals
But in this unit we will only be concerned with
drawing enough diagonals to make triangle.
Examples:
Divide the polygon into triangles to find the sum
of its angle measures.
1.
2.
If a 3-sided figure has 1• 180 =180˚
4-sided figure has 2• 180 = 360˚
5-sided figure has 3• 180 = 540˚
6-sided figure has 4• 180 = 720˚
Can you figure out...
7-sided figure
8-sided figure
What about a rule that works for any sided figure?
Does it work for Concave Polygons?
4-sided
5-sided
7-sided
Word Problems:
1. A truss bridge is supported by triangular frames. If
every triangular frame in a truss bridge is an isosceles
right triangle, what is the measure of each angle in one
of the frames?
(what is an isosceles right triangle?)
2. Each outer wall of the Pentagon in Washington D.C.
measures 921 feet. What is the measure of each angle
made by the Pentagon's outer walls?
3. The angle between the lines of sight from a lighthouse
to a tugboat and to a cargo ship is 27˚. The angle
between the lines of sight at the cargo ship is twice the
angle between the lines of sight at the tugboat. What are
the angles at the tugboat and at the cargo ship?