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

From the following picture, determine , and .

Plot12

Possible Answers:

y = 57.0 , x = 100.0

y = 123.0 , x = 80.0

y = 100.0 , x = 57.0

y = 237.0 , x = 280.0

y = 303.0 , x = 260.0

Correct answer:

y = 57.0 , x = 100.0

Explanation:

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

Plot12

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 .

$\\180 = y + 123.0 \\180 = x + 80.0$

Now let's solve for , and .

$\\180-123.0 = y + 123.0{\color{Red} -123.0} \\180-80.0 = x + 80.0{\color{Red} -80.0} \\y = 57.0 \\x = 100.0$

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Example Question #11 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine x and y.

$\uptext{x}$ Plot1

Possible Answers:

y = 97.0 , x = 71.0

y = 71.0 , x = 97.0

y = 83.0 , x = 109.0

y = 277.0 , x = 251.0

y = 263.0 , x = 289.0

Correct answer:

y = 97.0 , x = 71.0

Explanation:

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

Plot1

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 .

$\\180 = y + 83.0 \\180 = x + 109.0$

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

$\\180-83.0 = y +83.0{\color{Red} -83.0}\\180-109.0 = x+109.0{\color{Red} -109.0}$

$\\y = 97.0 \\x = 71.0$

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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

Example Question #11 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

All Common Core: High School - Geometry Resources

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