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Common Core: High School - Geometry : Inscribed and Circumscribed Circle of Triangles: CCSS.Math.Content.HSG-C.A.3

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Plot2

Possible Answers:

y = 100.0 , x = 111.0

y = 80.0 , x = 69.0

y = 260.0 , x = 249.0

y = 280.0 , x = 291.0

y = 111.0 , x = 100.0

Correct answer:

y = 100.0 , x = 111.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot2

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for , and .

$\\180 = y + 80.0 \\180 = x + 69.0$

Now let's solve for , and .

$\\180 -80.0= y + 80.0{\color{Red} -80.0} \\180-69.0 = x + 69.0{\color{Red} -69.0}$

$\\y = 100.0 \\x = 111.0$

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Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine and .

Plot3

Possible Answers:

y = 131.0 , x = 88.0

y = 272.0 , x = 229.0

y = 268.0 , x = 311.0

y = 92.0 , x = 49.0

y = 88.0 , x = 131.0

Correct answer:

y = 88.0 , x = 131.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot3

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for and .

$\\180 = y + 92.0 \\180 = x + 49.0$

Now let's solve for and .

$\\180-92.0 = y + 92.0{\color{Red} -92.0} \\180-49.0 = x + 49.0{\color{Red} -49.0}$

$\\y = 88.0 \\x = 131.0$

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Example Question #3 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine and .

Plot4

Possible Answers:

y = 63.0 , x = 94.0

y = 94.0 , x = 63.0

y = 297.0 , x = 266.0

y = 117.0 , x = 86.0

y = 243.0 , x = 274.0

Correct answer:

y = 63.0 , x = 94.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot4

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for and .

$\\180 = y + 117.0 \\180 = x + 86.0$

Now let's solve for and .

$\\180-117.0 = y + 117.0{\color{Red} -117.0} \\180-86.0 = x + 86.0{\color{Red} -86.0}$

$\\y = 63.0 \\x = 94.0$

Report an Error

Example Question #4 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine and .

Plot5

Possible Answers:

y = 108.0 , x = 85.0

y = 72.0 , x = 95.0

y = 85.0 , x = 108.0

y = 252.0 , x = 275.0

y = 288.0 , x = 265.0

Correct answer:

y = 108.0 , x = 85.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot5

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for and .

$\\180 = y + 72.0 \\180 = x + 95.0$

Now let's solve for and .

$\\180 -72.0= y + 72.0{\color{Red} -72.0} \\180 -95.0= x + 95.0{\color{Red} -95.0}$

$\\y = 108.0 \\x = 85.0$

Report an Error

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine and .

Plot6

Possible Answers:

y = 291.0 , x = 288.0

y = 108.0 , x = 111.0

y = 69.0 , x = 72.0

y = 249.0 , x = 252.0

y = 111.0 , x = 108.0

Correct answer:

y = 111.0 , x = 108.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot6

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for and .

$\\180 = y + 69.0 \\180 = x + 72.0$

Now let's solve for and .

$\\180-69.0 = y + 69.0{\color{Red} -69.0} \\180-72.0 = x + 72.0{\color{Red} -72.0} \\y = 111.0 \\x = 108.0$

Report an Error

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Plot7

Possible Answers:

y = 74.0 , x = 72.0

y = 108.0 , x = 106.0

y = 106.0 , x = 108.0

y = 254.0 , x = 252.0

y = 286.0 , x = 288.0

Correct answer:

y = 106.0 , x = 108.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot7

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for , and .

$\\180 = y + 74.0 \\180 = x + 72.0$

Now let's solve for , and .

$\\180 -74.0= y + 74.0{\color{Red} -74.0} \\180 -72.0= x + 72.0{\color{Red} -72.0} \\y = 106.0 \\x = 108.0$

Report an Error

Example Question #7 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Plot8

Possible Answers:

y = 266.0 , x = 292.0

y = 86.0 , x = 112.0

y = 68.0 , x = 94.0

y = 274.0 , x = 248.0

y = 94.0 , x = 68.0

Correct answer:

y = 94.0 , x = 68.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot8

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for , and .

$\\180 = y + 86.0 \\180 = x + 112.0$

Now let's solve for , and .

$\\180 -86.0= y + 86.0{\color{Red} -86.0} \\180 -112.0= x + 112.0{\color{Red} -112.0} \\y = 94.0 \\x = 68.0$

Report an Error

Example Question #7 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Plot9

Possible Answers:

y = 109.0 , x = 115.0

y = 65.0 , x = 71.0

y = 251.0 , x = 245.0

y = 289.0 , x = 295.0

y = 71.0 , x = 65.0

Correct answer:

y = 71.0 , x = 65.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot9

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for , and .

$\\180 = y + 109.0 \\180 = x + 115.0$

Now let's solve for , and .

$\\180-109.0 = y + 109.0{\color{Red} -109.0} \\180-115.0 = x + 115.0{\color{Red} -115.0} \\y = 71.0 \\x = 65.0$

Report an Error

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine \uptext{x}, and \uptext{y}.

Possible Answers:

Wrong Answer 3: y = 117.0 , x = 63.0

Correct Answer: y = 63.0 , x = 117.0

Wrong Answer 1: y = 243.0 , x = 297.0

Wrong Answer 2: y = 297.0 , x = 243.0

Wrong Answer 4: y = 117.0 , x = 63.0

Correct answer:

Correct Answer: y = 63.0 , x = 117.0

Explanation:

Explanation

INSERT PICTURE HERE

Since this polygon is inscribed within a circle, we know a few things.

The first thing we know is that the sum of all the interior angles must equal 360^{\circ}.

The last thing we know, the most important one is all opposite angles must equal 180^{\circ}.

Now we need to set up equations to solve for \uptext{x}, and \uptext{y}.

180 = y + 117.0

180 = x + 63.0

Now let's solve for \uptext{x}, and \uptext{y}.

y = 63.0

x = 117.0

Report an Error

Example Question #10 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Plot11

Possible Answers:

y = 103.0 , x = 74.0

y = 254.0 , x = 283.0

y = 286.0 , x = 257.0

y = 74.0 , x = 103.0

y = 106.0 , x = 77.0

Correct answer:

y = 74.0 , x = 103.0

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot11

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ .

Now we need to set up equations to solve for , and .

$\\180 = y + 106.0 \\180 = x + 77.0$

Now let's solve for , and .

$\\180 -106.0= y + 106.0{\color{Red} -106.0} \\180-77.0 = x + 77.0{\color{Red} -77.0} \\y = 74.0 \\x = 103.0$

Report an Error

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Inscribed and Circumscribed Circle of Triangles: CCSS.Math.Content.HSG-C.A.3

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #3 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #4 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #7 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #7 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #10 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

All Common Core: High School - Geometry Resources

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