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Common Core: High School - Geometry : Relationships Between Angles, Radii, Chords, and Diameters of Circles: CCSS.Math.Content.HSG-C.A.2

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

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Example Questions

Example Question #1 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $22 ^{\circ}$ $\displaystyle 22 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$22 ^{\circ}$ $\displaystyle 22 ^{\circ}$

$158 ^{\circ}$ $\displaystyle 158 ^{\circ}$

$248 ^{\circ}$ $\displaystyle 248 ^{\circ}$

$68 ^{\circ}$ $\displaystyle 68 ^{\circ}$

$338 ^{\circ}$ $\displaystyle 338 ^{\circ}$

Correct answer:

$22 ^{\circ}$ $\displaystyle 22 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $22 ^{\circ}$ $\displaystyle 22 ^{\circ}$

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Example Question #2 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $11 ^{\circ}$ $\displaystyle 11 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$169 ^{\circ}$ $\displaystyle 169 ^{\circ}$

$79 ^{\circ}$ $\displaystyle 79 ^{\circ}$

$11 ^{\circ}$ $\displaystyle 11 ^{\circ}$

$349 ^{\circ}$ $\displaystyle 349 ^{\circ}$

$259 ^{\circ}$ $\displaystyle 259 ^{\circ}$

Correct answer:

$11 ^{\circ}$ $\displaystyle 11 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $11 ^{\circ}$ $\displaystyle 11 ^{\circ}$

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Example Question #3 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $31 ^{\circ}$ $\displaystyle 31 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$239 ^{\circ}$ $\displaystyle 239 ^{\circ}$

$59 ^{\circ}$ $\displaystyle 59 ^{\circ}$

$329 ^{\circ}$ $\displaystyle 329 ^{\circ}$

$31 ^{\circ}$ $\displaystyle 31 ^{\circ}$

$149 ^{\circ}$ $\displaystyle 149 ^{\circ}$

Correct answer:

$31 ^{\circ}$ $\displaystyle 31 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $31 ^{\circ}$ $\displaystyle 31 ^{\circ}$

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Example Question #4 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $70 ^{\circ}$ $\displaystyle 70 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$20 ^{\circ}$ $\displaystyle 20 ^{\circ}$

$200 ^{\circ}$ $\displaystyle 200 ^{\circ}$

$70 ^{\circ}$ $\displaystyle 70 ^{\circ}$

$290 ^{\circ}$ $\displaystyle 290 ^{\circ}$

$110 ^{\circ}$ $\displaystyle 110 ^{\circ}$

Correct answer:

$70 ^{\circ}$ $\displaystyle 70 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $70 ^{\circ}$ $\displaystyle 70 ^{\circ}$

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Example Question #3 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $12 ^{\circ}$ $\displaystyle 12 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$12 ^{\circ}$ $\displaystyle 12 ^{\circ}$

$168 ^{\circ}$ $\displaystyle 168 ^{\circ}$

$258 ^{\circ}$ $\displaystyle 258 ^{\circ}$

$78 ^{\circ}$ $\displaystyle 78 ^{\circ}$

$348 ^{\circ}$ $\displaystyle 348 ^{\circ}$

Correct answer:

$12 ^{\circ}$ $\displaystyle 12 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $12 ^{\circ}$ $\displaystyle 12 ^{\circ}$

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Example Question #6 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

If the arc measure is $59 ^{\circ}$ $\displaystyle 59 ^{\circ}$ what is the measure of the central angle?

Possible Answers:

$121 ^{\circ}$ $\displaystyle 121 ^{\circ}$

$301 ^{\circ}$ $\displaystyle 301 ^{\circ}$

$211 ^{\circ}$ $\displaystyle 211 ^{\circ}$

$31 ^{\circ}$ $\displaystyle 31 ^{\circ}$

$59 ^{\circ}$ $\displaystyle 59 ^{\circ}$

Correct answer:

$59 ^{\circ}$ $\displaystyle 59 ^{\circ}$

Explanation:

The central angle is the same as the arc measure.

So the answer is $59 ^{\circ}$ $\displaystyle 59 ^{\circ}$

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Example Question #7 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

What is the measure of an inscribed angle with an arc measurement of $12 ^{\circ}$ $\displaystyle 12 ^{\circ}$?

Possible Answers:

$48\degree$ $\displaystyle 48\degree$

$12\degree$ $\displaystyle 12\degree$

$24\degree$ $\displaystyle 24\degree$

$6\degree$ $\displaystyle 6\degree$

$13\degree$ $\displaystyle 13\degree$

Correct answer:

$6\degree$ $\displaystyle 6\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=12 \cdot \frac{1}{2} \\\\=6$ $\displaystyle \\=12 \cdot \frac{1}{2} \\\\=6$

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Example Question #8 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

What is the measure of an inscribed angle with an arc measurement of $42 ^{\circ}$ $\displaystyle 42 ^{\circ}$.

Possible Answers:

$21\degree$ $\displaystyle 21\degree$

$42\degree$ $\displaystyle 42\degree$

$84\degree$ $\displaystyle 84\degree$

$43\degree$ $\displaystyle 43\degree$

$168\degree$ $\displaystyle 168\degree$

Correct answer:

$21\degree$ $\displaystyle 21\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=42 \cdot \frac{1}{2} \\\\=21$ $\displaystyle \\=42 \cdot \frac{1}{2} \\\\=21$

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Example Question #4 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

What is the measure of an inscribed angle with an arc measurement of $86 ^{\circ}$ $\displaystyle 86 ^{\circ}$?

Possible Answers:

$344\degree$ $\displaystyle 344\degree$

$86\degree$ $\displaystyle 86\degree$

$172\degree$ $\displaystyle 172\degree$

$87\degree$ $\displaystyle 87\degree$

$43\degree$ $\displaystyle 43\degree$

Correct answer:

$43\degree$ $\displaystyle 43\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=86 \cdot \frac{1}{2} \\\\=43$ $\displaystyle \\=86 \cdot \frac{1}{2} \\\\=43$

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Example Question #10 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

What is the measure of an inscribed angle with an arc measurement of $54 ^{\circ}$ $\displaystyle 54 ^{\circ}$?

Possible Answers:

$108\degree$ $\displaystyle 108\degree$

$216\degree$ $\displaystyle 216\degree$

$54\degree$ $\displaystyle 54\degree$

$55\degree$ $\displaystyle 55\degree$

$27\degree$ $\displaystyle 27\degree$

Correct answer:

$27\degree$ $\displaystyle 27\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=54 \cdot \frac{1}{2} \\\\=27$ $\displaystyle \\=54 \cdot \frac{1}{2} \\\\=27$

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Relationships Between Angles, Radii, Chords, and Diameters of Circles: CCSS.Math.Content.HSG-C.A.2

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #2 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #3 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #4 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #3 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #6 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #7 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #8 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #4 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

Example Question #10 : Relationships Between Angles, Radii, Chords, And Diameters Of Circles: Ccss.Math.Content.Hsg C.A.2

All Common Core: High School - Geometry Resources

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