Category 3 Day 1 Review

Category 3 Day 1 Review

​Polygons & The Equation of a Circle

This review is all about the interior and exterior angles of polygons, as well as, the equation of a circle.

Use this review to help you fill in the blanks on your work sheets and to help solve the given problems.

Interior Angle Formula:

Sum = (n-2)180

*n= number of sides the polygon has

​Interior Sum Formula:

Interior Angles of Polygons

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Multiple Choice

How do you find the sum of the interior angles of a polygon?

• n-2

• (n-2)180

• $$\frac{\left(n-2\right)180}{n}$$

• $$\frac{\left(n-2\right)180}{180}$$

Multiple Choice

How do you find the measure of one of the interior angles of a polygon?

• n-2

• (n-2)180

• $$\frac{\left(n-2\right)180}{n}$$

• $$\frac{\left(n-2\right)180}{180}$$

Fill in the Blank

What is the sum of the interior angles of a dodecagon?

Fill in the Blank

What is the sum of the interior angles of a 54-gon? [Just type in your answer]

Match

Match the following regular polygons to the measure of thier interior angle.

• 120

• 150

• 162

• 165.6

• 175.5

Hexagon

12-gon

20-gon

25-gon

80-gon

• Hexagon

• 12-gon

• 20-gon

• 25-gon

• 80-gon

Interior Angles: Solving Numeric and Algebraic Problems

​Steps:

1) Find the interior sum of the given polygon.

2) Find the total number of x's that you have

3) Combine all of the given numbers (do not forget the 90 if you are given a right angle box)

4) Set up your equation as: x's + numbers = sum

x + 458 = 540

-458 -458

x = 82

Equation:

1) Sum = (5-2)180 = 540

*polygon has 5 sides

2) x = 1x or x

3) #s= 110 + 92 + 152 + 104 = 458

Example: Solve for x.

21x + 321 = 720

-231 -321

21x = 399

÷21 = ÷21

x=19

Equation:

1) Sum = (6-2)180 = 720

2) x = 9x + 5x + 7x = 21x

3) #s = 90 - 19 + 111 +8 +128 + 3 = 321

Solve for x.

2x + 974 = 1260

-974 -974

2x = 286

÷2 = ÷2

x = 143

​Equation:

Sum = (9-2)180 = 1,260

x = 2x

Two remaining angles are congruent

# = 138 + 154 + 145+ 132 + 128 + 147 + 130 = 974

The measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°, and 130°. If the two remaining angles are equal in measure, what is the measure of each angle?

Fill in the Blank

Solve for x.

Fill in the Blank

Solve for x. [Type your answer in the box]

Fill in the Blank

Two interior angles of a hexagon measure $$86\degree$$  and $$98\degree$$ . The other four angles are congruent.

What is the measure of each of the four congruent angles?

Exterior Angles of Regular Polygons

360 degrees

*It does not matter how many sides. The sum is ALWAYS 360!

​Exterior Sum:

Exterior Angles of Polygons

​2) 28-gon

1) Nonagon

Find the Exterior Angle:

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Multiple Choice

What is the exterior angle measure of a regular 20-gon?

• 18 degrees

• 20 degrees

• 3,240 degrees

• 162 degrees

x + # = 360

Equation:

1) Sum = 60

2) Find the number of x's

3) Combine the numbers

Steps:

Solving Exterior Angle Problems

Sum = 360

y= 1y or y

#= 70+60+65+40= 235

y+235=360

-235 -235

y=125

sum = 360 *180-71=109

x= 10x + 13x+ 8x=31x

#= 6-2-1+109=112

31x+112=360

-112 -112

31x=248

÷31 ÷31

x=8

Fill in the Blank

Solve for x.

Type your numeric answer in the box.

​Interior Angle:

​Exterior Angle:

Finding the number of sides of a polygon

​Exterior Angle 6 degrees:

Find the number of sides of each polygon:

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Multiple Choice

How many sides does a polygon have if its exterior angle is 24 degrees?

• 24

• 156

• 15

• 7.5

Multiple Choice

How many sides does a regular polygon have if it's interior angle is $$162\degree$$ ?

• 162

• 18

• 20

• 10

Equation of A Circle

The next slides are all going to cover the equation of a circle.

(h,k) = Center of the circle

• Always opposite in the equation

r= radius

Important:

Equation:

Equation of a Circle:

Identify the Center & Radius from the equation:

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​https://emediava.org/l/37103

Creating the Equation of a Circle:

Multiple Choice

What is the equation of a circle whose center is (-11,15) and has a radius of 10?

• $$\left(x-11\right)^2+\left(y+15\right)^2=100$$

• $$\left(x+11\right)^2+\left(y-15\right)^2=100$$

• $$\left(x-11\right)^2+\left(y+15\right)^2=10$$

• $$\left(x+11\right)^2+\left(y-15\right)^2=10$$

Multiple Choice

What is the equation of a circle whose diameter is 12 and has a center (7,6)

• $$\left(x+7\right)^2+\left(y+6\right)^2=36$$

• $$\left(x-7\right)^2+\left(y-6\right)^2=36$$

• $$\left(x+7\right)^2+\left(y+6\right)^2=144$$

• $$\left(x-7\right)^2+\left(y-6\right)^2=144$$

Practice Questions

The following questions are all practice questions of the concepts reviewed throughout this lesson.

Match

Match the following formulas to what they help find.

• $$\frac{360}{ext\ \angle}$$

• $$\frac{360}{n}$$

• $$360$$

• $$\frac{\left(n-2\right)180}{n}$$

• $$\left(n-2\right)180$$

Number of Sides

Exterior Angle

Exterior Sum

Interior Angle

Interior Sum

• Number of Sides

• Exterior Angle

• Exterior Sum

• Interior Angle

• Interior Sum

Multiple Choice

Given the equation of a circle is $$\left(x-3\right)^2+\left(y-5\right)^2=36$$ , which correctly identifies the center and the radius?

• Center: (3, 5)

  Radius: 36

• Center: (-3,-5)

  Radius: 36

• Center: (3,5)

  Radius: 6

• Center: (-3,-5)

  Radius: 6

Fill in the Blank

What is the radius of the circle with the equation $$\left(x+5\right)^2+\left(y-9\right)^2=144$$

Fill in the Blank

What is the center of a circle whose equation is $$\left(x+3\right)^2+\left(y-2\right)^2=4$$

Type your answer in as (x,y)

(

-

,

)

Multiple Choice

What is the interior sum of the angles of a 36-gon?

• 6,120 degrees

• 6,480 degrees

• 180 degrees

• 170 degrees

Fill in the Blank

What is the interior sum of the angles of a heptagon?

Multiple Choice

What is the measure of each interior angle of a regular pentagon?

• 108 degrees

• 540 degrees

• 72 degrees

• 180degrees

Fill in the Blank

What is the $$m\angle HJK$$ ?

Multiple Choice

What is the sum of the exterior angles of a regular nonagon?

• 45

• 360

• 180

• 135

Multiple Choice

What is the measure of each exterior angle of a regular 40-gon?

• 9 degrees

• 6,840 degrees

• 7,200 degrees

• 171 degrees

Fill in the Blank

Solve for x. Type your numeric answer in the box.

Fill in the Blank

Solve for x. Type your numeric answer in the box.

Fill in the Blank

Solve for x.

Multiple Choice

How many sides does a regular polygon have if the exterior angle is 24 degrees?

• 24

• 156

• 15

• 7.5

Multiple Choice

If an interior angle of a regular polygon measures 150 degreesm then how many sides does it have?

• 150

• 30

• 15

• 12

Multiple Choice

What is the equation of a circle whose center is (-4,9) and has a radius of 18.

• $$\left(x-4\right)^2+\left(y+9\right)^2=18$$

• $$\left(x-4\right)^2+\left(y+9\right)^2=324$$

• $$\left(x+4\right)^2+\left(y-9\right)^2=18$$

• $$\left(x+4\right)^2+\left(y-9\right)^2=324$$

Multiple Choice

A circle has a diameter of 24 and a center at the point (-5,1). What is its equation?

• $$\left(x-5\right)^2+\left(y+1\right)^2=324$$

• $$\left(x+5\right)^2+\left(y-1\right)^2=144$$

• $$\left(x-5\right)^2+\left(y+1\right)^2=144$$

• $$\left(x+5\right)^2+\left(y-1\right)^2=324$$