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

## Example Questions

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

From the following picture, determine , and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for , and .

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

From the following picture, determine , and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for , and .

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

From the following picture, determine  and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for   and .

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

From the following picture, determine  and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for  and .

### Example Question #5 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine  and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for  and .

### Example Question #6 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine  and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for   and .

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

From the following picture, determine , and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for , and .

### Example Question #8 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for , and .

### Example Question #9 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine , and .

Explanation:

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 .

The last thing we know, the most important one is all opposite angles must equal .

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

Now let's solve for , and .

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

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

Wrong Answer 2: y = 297.0 , x = 243.0

Wrong Answer 4: y = 117.0 , x = 63.0

Wrong Answer 3: y = 117.0 , x = 63.0

Wrong Answer 1: y = 243.0 , x = 297.0

Correct Answer: y = 63.0 , x = 117.0

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

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