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

From the following picture, determine $\displaystyle x$, and $\displaystyle y$.

Plot2

$\displaystyle y = 80.0 , x = 69.0$

$\displaystyle y = 111.0 , x = 100.0$

$\displaystyle y = 280.0 , x = 291.0$

$\displaystyle y = 100.0 , x = 111.0$

$\displaystyle y = 260.0 , x = 249.0$

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

From the following picture, determine $\displaystyle x$, and $\displaystyle y$.

Plot2

$\displaystyle y = 80.0 , x = 69.0$

$\displaystyle y = 111.0 , x = 100.0$

$\displaystyle y = 280.0 , x = 291.0$

$\displaystyle y = 100.0 , x = 111.0$

$\displaystyle y = 260.0 , x = 249.0$

Report an Error Copyright Notice

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

From the following picture, determine $\displaystyle x$, and $\displaystyle y$.

Plot2

Your answer:

$\displaystyle y = 80.0 , x = 69.0$

Your answer:

$\displaystyle y = 111.0 , x = 100.0$

Your answer:

$\displaystyle y = 280.0 , x = 291.0$

Your answer:

$\displaystyle y = 260.0 , x = 249.0$

Correct answer:

$\displaystyle y = 100.0 , x = 111.0$

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 $360^{\circ}$ $\displaystyle 360^{\circ}$.

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

Now we need to set up equations to solve for $\displaystyle x$, and $\displaystyle y$.

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

Now let's solve for $\displaystyle x$, and $\displaystyle y$.

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

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

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

From the following picture, determine $\displaystyle x$ and $\displaystyle y$.

Plot3

$\displaystyle y = 88.0 , x = 131.0$

$\displaystyle y = 92.0 , x = 49.0$

$\displaystyle y = 268.0 , x = 311.0$

$\displaystyle y = 131.0 , x = 88.0$

$\displaystyle y = 272.0 , x = 229.0$

Report an Error Copyright Notice

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

From the following picture, determine $\displaystyle x$ and $\displaystyle y$.

Plot3

Your answer:

$\displaystyle y = 92.0 , x = 49.0$

Your answer:

$\displaystyle y = 268.0 , x = 311.0$

Your answer:

$\displaystyle y = 131.0 , x = 88.0$

Your answer:

$\displaystyle y = 272.0 , x = 229.0$

Correct answer:

$\displaystyle y = 88.0 , x = 131.0$

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 $360^{\circ}$ $\displaystyle 360^{\circ}$.

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

Now we need to set up equations to solve for $\displaystyle x$ and $\displaystyle y$.

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

Now let's solve for $\displaystyle x$ and $\displaystyle y$.

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

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

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

All Common Core: High School - Geometry Resources

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

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

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

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

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