Mod 7.1 Interior and Exterior Angles

Author:Patricia Tarleton, Tim Brzezinski, GeoGebra Team, Steve Phelps

Topic:Angles

Triangle Sum Theorem

Change the angles of the above triangle. What is the sum of all three interior angles of the triangle?

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When will the sum of the interior angles of a triangle add up to 180 degrees?

Select all that apply

A
The sum of the interior angles of a triangle will sometimes be 180 degrees.
B
The sum of the interior angles of a triangle will always be 180 degrees.
C
The sum of the interior angles of a triangle never will be 180 degrees.

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Is it possible to create a triangle that the interior angles do not add up to 180 degrees?

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Notice when the sides of the angles are adjacent and the vertices meet at one point, they form a straight angle.

What is the measure of a straight angle?

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Take Note

Triangle Sum Theorem: The sum of the angle measures of a triangle is 180 degrees.

How to find the sum of the interior angles of polygons. Be sure to pause video if needed and take notes.

Take Note:

Polygon angle sum theorem: The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180^o

Polygon Angle Sum

Using the slides on the above image, determine the sum of the interior angles of a dodecagon (12 sided polygon).

Select all that apply

A
2160^o
B
1800^o
C
None of the above.

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Using the slides on the above image, determine the sum of the interior angles of a hexagon (6 sided polygon).

Select all that apply

A
1080^o
B
540^o
C
720^o

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Using the slides on the above image determine the sum of the interior angles of a pentagon (5 sided polygon)

Select all that apply

A
540^o
B
900^o
C
360^o

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To determine the unknown angles of this pentagon we need to first determine the sum of the interior angles of a pentagon using the polygon angle sum theorem. (n-2)180[sup]o

[/sup]We determined that measure in the previous question and found the sum of the interior angles of a pentagon is 540[sup]o

[/sup]Write an equation adding up all interior angles and set it equal to 540[sup]o
[/sup]Solve for x[sup]o[/sup] — To determine the unknown angles of this pentagon we need to first determine the sum of the interior angles of a pentagon using the polygon angle sum theorem. (n-2)180^oWe determined that measure in the previous question and found the sum of the interior angles of a pentagon is 540^oWrite an equation adding up all interior angles and set it equal to 540^oSolve for x^o

What is the measure of angle x in the pentagon above?

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Take Notes as you watch video. Pause if needed.

Take notes, pausing video as needed. Also look for her mistake, one time she refers to opposite angles a and b as adjacent angles. Can you find the mistake?

Take note of Theorem

Solve the following

Looking at image above

What is the ? Set up the equation to solve for x. Solve for x, then substitute that value for x into the equation to determine the measure of angle B.

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