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

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Question

From the following picture, determine x and y.

$\uptext{x}$

Answer

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 .

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

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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Question

From the following picture, determine , and .

Answer

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 , 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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Question

From the following picture, determine and .

Answer

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 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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Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

$\y = 63.0 \x = 94.0$

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Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

$\y = 108.0 \x = 85.0$

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Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

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Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

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Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

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Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

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Question

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

Answer

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

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Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

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Question

From the following picture, determine , and .

Answer

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 , 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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Question

From the following picture, determine x and y.

$\uptext{x}$

Answer

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 .

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

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

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

$\y = 97.0 \x = 71.0$

Compare your answer with the correct one above

Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

$\y = 100.0 \x = 111.0$

Compare your answer with the correct one above

Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

$\y = 88.0 \x = 131.0$

Compare your answer with the correct one above

Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

$\y = 63.0 \x = 94.0$

Compare your answer with the correct one above

Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

$\y = 108.0 \x = 85.0$

Compare your answer with the correct one above

Question

From the following picture, determine and .

Answer

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 and .

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

Now let's solve for and .

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

Compare your answer with the correct one above

Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

Compare your answer with the correct one above

Question

From the following picture, determine , and .

Answer

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 , and .

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

Now let's solve for , and .

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

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