Download Module 7 Lesson 1 Angles of Polygons Remediation Notes Slide 1

Module 7 Lesson 1 Angles of Polygons Remediation Notes
Slide 1:
“Please pause this video and take a moment to match up the names of the polygons with the
correct number of sides. Right your answers down so you can check them.”
Slide 2:
“Great! How did you do? We know a triangle has three sides, a heptagon has seven sides, an
octagon has eight sides, pentagons have five, hexagons have six, and all squares have four
sides.”
Slide 3:
“We also want to review the parts of a polygon. Remember that each place that two sides join is
called a vertex. This polygon has many vertices. In fact, it has five. A, B, C, D, and E all
represent a vertex. In between the vertices are sides. So, this would be side CD, and this would
be side DE.”
Slide 4:
“We’re also very interested in naming polygons so that we know exactly which polygon we are
talking about. In order to name a polygon, you need to use all letters of each vertex. Simply pick
a place to start – I will start with P – and you either go clockwise or counterclockwise with the
letters. I’m going to go clockwise, so the name of this polygon could be PQRST. Now, you can
start from any letter. I could start from S and go counterclockwise, and I could name this
polygon SRQPT. That’s perfectly fine as long as they are in order either clockwise or
counterclockwise and you include all letters.”
Slide 5:
“We also need to find the sum of the interior angles of a polygon. There are three methods for
you to choose from. Please pick the method that works best for you.”
Slide 6:
“Method one is filling out a table. We list the polygon’s name and the number of sides. We then
fill in the number of triangles that can be formed inside of that polygon that do not overlap. We
multiply the number of triangles formed by one hundred eighty.”
Slide 7:
“Method two is simple, especially if you have polygons with many sides. If I have a ninety-five
sided polygon, all I need to do is stick ninety-five in here for ‘n’, which is the number of sides,
and I would do ninety-five minus two and multiply that by one hundred eighty degrees to get the
sum of the measures of the interior angles in a polygon with ninety-five sides.”
Slide 8:
“Method three is confusing at first, but if you know that the sum of the interior angles of every
triangle is one hundred eighty degrees, you can say that every time you add a side to the triangle,
you add one hundred eighty degrees. A triangle is one hundred eighty degrees. If I add a side, it
is a rectangle, and now I have three hundred sixty degrees. If I add another side, I have a
pentagon. I have three sixty plus one eighty, or one eighty plus one eighty plus one eighty, which
is five hundred forty degrees.”
Slide 9:
“Let’s practice. Find the measure of an interior angle and an exterior angle for the polygon. We
have eighteen sides, so using the formula ‘n’ minus two times one eighty, I would plug in
eighteen for ‘n’. Eighteen minus two is sixteen, times one hundred eighty gives me two thousand
eight hundred eighty degrees. If I want to know the measure of one angle inside of the polygon, I
take two thousand eight hundred eighty degrees divided by eighteen, which means every little
angle in here is one hundred sixty degrees.”
Slide 10:
“Pause the video and try to find the measures of the missing angle in these videos. In the
trapezoid, the ‘x’ value is seventy-two. In our pentagon, the measure of angle T and the measure
of angle S are both one hundred three degrees because they are marked congruent.”
Slide 11:
“Take a moment to pause this video and find the measure of the missing angle. Great job! It
should be one hundred seven degrees.”
Slide 12:
“Finally, let’s look at the Polygon Exterior Angle-Sum Theorem. It states that the sum of the
measures of the exterior angles of any polygon is three hundred sixty degrees. It doesn’t matter
how many sides the polygon has; all exterior angles add up to three hundred sixty degrees.”