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## Homework 2 Central Angles Arc Measures

Homework 2 Central Angles Arc Measures - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Assignment, Arc length and sector area, Geometry 10 2 angles and arcs, 11 arcs and central angles, Geometry unit 10 notes circles, 11 arcs and central angles, Homework section 9 1.

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## 1. Assignment

2. arc length and sector area, 3. geometry 10-2 angles and arcs, 4. 11-arcs and central angles, 5. geometry unit 10 notes circles, 6. 11-arcs and central angles, 7. homework section 9-1.

## Algebra and Pre-Algebra

## Measures of arcs and central angles

We can use a few more theorems to find the measures of arcs and central angles of circles. Let’s begin by stating a few theorems:

THEOREM: The measure of a central angle is equal to the measure of the arc it intersects.

THEOREM: The measure of a major arc (an arc greater than a semicircle) is equal to \(360^\circ \) minus the measure of the corresponding minor arc.

THEOREM: Vertical angles are equal.

EXAMPLE: Find the measure of the arc \(\widehat {IKH}\)

SOLUTION: \(\widehat {IKH}\) is a major arc, so, by a theorem above, its measure is \(360^\circ - m\widehat {IH}\). Then we must find the measure of \(\widehat {IH}\).

Again, by a theorem above, we know that the measure of the central angle corresponding to \(\widehat {JK}\) must be \(70^\circ \). Now we can conclude, by the fact that straight angles measure \(180^\circ \), that the central angle corresponding to \(\widehat {IH}\) equals \(180 - 70 - 70 = 40\). That is, \(m\widehat {IH} = 40^\circ \).

So we can conclude that \(m\widehat {IKH} = 360^\circ - 40^\circ = 320^\circ \).

EXAMPLE: Find \(m\angle JKI\)

SOLUTION: Since \(\widehat {FKG} = 50^\circ \), we can conclude, by a theorem above, that \(\angle FKG = 50^\circ \). Then, by the vertical angle theorem, we know that \(\angle JKL = \angle FKG\). That is, \(\angle JKL = 50^\circ \).

Below you can download some free math worksheets and practice.

Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.

This free worksheet contains 10 assignments each with 24 questions with answers. Example of one question:

Watch bellow how to solve this example:

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## CENTRAL ANGLES AND ARC MEASURES

1. A central angle is an angle with its vertex at the center of the circle and its two sides are radii.

2. For example : m ∠POQ is a central angle in circle P shown below.

3. The sum of all central angle is 360 °.

4. The measure of the arc formed by the endpoints of a central angle is equal to the degree of the central angle.

In the above diagram,

m ∠arc PQ = 85 °

m ∠arc PRQ = 360 ° - 85 ° = 275 °

5. The measure of the arc formed by the endpoints of the diameter is equal to 180 ° .

m∠arc PRQ = 180 °

Example 1 :

From the diagram shown above, find the following arc measures.

(i) m ∠arc BC

(ii) m∠arc ABC

(i) m ∠arc BC :

AB is the diameter of the above circle.

m∠arc AB = 180 °

m∠arc BC + m∠arc CA = 180 °

m∠arc BC + 123 ° = 180 °

m∠arc BC = 57 °

(ii) m∠arc ABC :

m∠arc ABC = m ∠arc AB + m ∠arc BC

= 180 ° + 57 °

Example 2 :

From the diagram shown above, find the following measures.

(i) m ∠arc CD

(iii) m∠arc BD

(iv) m∠arc ABC

(v) m∠arc CBD

(i) m ∠arc CD :

m∠AOB and m ∠COD are vertical angles.

m ∠COD = m ∠AOB

m ∠arc CD = m ∠arc AB

m∠arc CD = 55 °

(ii) m∠AOC :

BC is the diameter of the above circle.

m∠arc BAC = 180 °

m∠arc BA + m∠arc AC = 180 °.

55 ° + m∠arc AC = 180 °.

m∠arc AC = 125 °.

m∠AOC = 125 °.

(iii) m∠arc BD :

m∠BOD and m ∠AOC are vertical angles.

m ∠BOD = m ∠AOC

m ∠BOD = 125 °

m∠arc BD = 125°

(iv) m∠arc ABC :

m∠arc ABC = m∠arc ABD + m∠arc DC

= 180 ° + 55 °

(v) m∠arc CBD :

m∠arc CBD = m∠arc CAB + m∠arc BD

= 180 ° + 125 °

Example 3 :

Find the value of x in the diagram shown below.

From the diagram shown above, find the m ∠arc QTR.

Find m ∠arc QP :

PS is the diameter of the above circle.

m ∠arc PTS = 180 °

m∠arc PT + m∠arc TS = 180°

135 ° + m∠arc TS = 180°

m∠arc TS = 45°

Find m ∠arc QTR :

m∠QTR = m ∠arc QT + m ∠arc TS + m ∠arc SR

= 180 ° + 45 ° + 81 °

Example 4 :

m ∠BOD, m ∠BOE and m ∠BOC

Find m ∠BOD :

In the circle above,

m ∠arc AB + m ∠arc BCD + m ∠arc DE + m ∠arc EA = 360 °

60 ° + m ∠arc BCD + 86 ° + 154 ° = 360 °

m ∠arc BCD + 300 ° = 360 °

m ∠arc BCD = 60 °

m ∠BOD = 60 °

Find m ∠BOE :

m ∠BOE = m ∠arc BCD + m∠arc DE

= 60 ° + 86 °

Find m ∠BOC :

In the above diagram, m∠BOC = m ∠COD.

m∠BOC + m∠COD = m∠BOD

m∠BOC + m∠BOC = m∠BOD

2m∠BOC = 60 °

m∠BOC = 30 °

Example 5 :

m ∠ KOL and m∠arc MNK

In the diagram above, m∠JON and ∠KOM are vertical angles.

m∠KOM = m ∠KOM

m∠KOM = 126 °

m∠KOL + m ∠LOM = 126 °

In the above diagram, m∠KOL = m ∠LOM.

m∠KOL + m∠KOL = 126°

2m∠KOL = 126°

m ∠ KOL = 63°

Find m ∠arc MNK :

m∠arc MNK = 360 ° - m ∠arc KLM

m∠arc MNK = 360° - m∠KOM

m∠arc MNK = 360° - 126 °

m∠arc MNK = 234 °

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- 20. Multiple Choice Edit 1 minute 1 pt Which is true of a minor arc? It forms half a circle. It forms a whole circle. It measures greater than 180 degrees. It measures less than 180 degrees.
- 21. Multiple Choice Edit 1 minute 1 pt Which is true of a major arc? Forms half a circle. Forms a whole circle. Measures greater than 180 degrees. Measures less than 180 degrees.

What is the measure of ∠PTQ?

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## COMMENTS

You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: 10.2 HW Name: Unit 10: Circles Date: Per: Homework 2: Central Angles & Arc Measures ** This is a 2-page document! " Directions: Find the following arc measures. 1. 2. 127 * D166 M MJL в MJML mBC ABC 3.

¥ h) Minor Arc: I i) Major Arc: H LJ j) Semicircle: 0 91 * k) Central Angle: * l) Inscribed Angle: 15) 2 225 IT Z 0(.pg z c Z, 20 .25 IT (Ð3.G2m C = C : q T 'V 28.21m ,oqTT Z 3212.85) 20 Directions: Use the area and circumference formulas to find the radius or diameter. 6. Find the radius of a circle with an area of 615.75 square kilometers. A

please solve the question. unit 10: circles homework 2: Central angles, arc measures, and arc length. ... 2.4K answers. 5.2M people helped. report flag outlined. Answer: Step-by-step explanation: (9x-22) + 61 + (5x-7) + 34 = 360. 14x = 294.

Final answer: In a circle, a central angle subtends an arc. While points along a radius rotate through the same angle, points farther from the center trace a larger arc. A great example is the movement of an analog clock's hour hand. Explanation: The question refers to central angles and arc measures, essential concepts in geometry.

538 Chapter 10 Circles 10.2 Lesson WWhat You Will Learnhat You Will Learn Find arc measures. Identify congruent arcs. Prove circles are similar. Finding Arc Measures A central angle of a circle is an angle whose vertex is the center of the circle. In the diagram, ∠ACB is a central angle of ⊙C. If m∠ACB is less than 180°, then the points on ⊙C that lie in the interior of ∠ACB

Inscribed angle. An angle whose vertex is on the circle and each side of the angle intersects the circle in another point. Arc. A portion of the circumference of the circle. Minor arc. An arc of a circle having a measure less than 180°. Major arc. An arc of a circle having a measure greater than 180°.

Adopted from All Things Algebra by Gina Wilson. Lesson 10.2 Central Angles and Arc MeasuresUnit 10 Circles

About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...

of the related minor arc. A is an arc whose central angle measures 180 8. A semicircle is named by three points. Its measure is 180 8. semicircle measure of a major arc measure of a minor arc major arc minor arc 11.3 Arcs and Central Angles LOOK BACK For the definition of a central angle, see p. 454. Student Help Name the red arc and identify ...

Homework 2 Central Angles Arc Measures - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Assignment, Arc length and sector area, Geometry 10 2 angles and arcs, 11 arcs and central angles, Geometry unit 10 notes circles, 11 arcs and central angles, Homework section 9 1.

THEOREM: The measure of a central angle is equal to the measure of the arc it intersects. THEOREM: The measure of a major arc (an arc greater than a semicircle) is equal to 360∘ 360 ∘ minus the measure of the corresponding minor arc. THEOREM: Vertical angles are equal. EXAMPLE: Find the measure of the arc IKHˆ I K H ^.

Find an answer to your question unit 10: circles homework 2 central angles & arc measures Number 15 See what teachers have to say about Brainly's new learning tools! WATCH ... Answer: Arc DBC is actually 221, everything else he got right. Step-by-step explanation: The entire circle equals 360, but not DBC, because its not the whole circle. ...

3. The sum of all central angle is 360°. 4. The measure of the arc formed by the endpoints of a central angle is equal to the degree of the central angle. In the above diagram, m∠arc PQ = 85°. m∠arc PRQ = 360° - 85° = 275°. 5. The measure of the arc formed by the endpoints of the diameter is equal to 180°.

an arc has a degree measure and a length; L (ab) = x°/360° (2 (pi)r) Arc Addition Postulate. mAB + mBC = mAC. Congruent Arcs and Angles Theorem. minor arcs are congruent iff their central angles are congruent. Study with Quizlet and memorize flashcards containing terms like 360° Theorem, Central Angle, Minor Arc (AB) and more.

The arc measure is equal to the measure of the central angle that is formed. Arc lengths are the length of the arc formed by a central angle. The arc length is equal to the circumference of the circle, divided by the measure of the central angle. For example, if a central angle of 104° is formed, the arc measure would be 104° and the arc ...

Central Angles and Arc Measures quiz for 10th grade students. Find other quizzes for Mathematics and more on Quizizz for free! Skip to Content Enter code. Log in. Sign up. Enter code ... Show Answers. See Preview. 1. Multiple Choice. Edit. 1 minute. 1 pt. 1. measure of arc JK. 339. 159. 201. 21. 2. Multiple Choice. Edit. 1 minute. 1 pt. 1 ...

The central angle (127 degrees) is the angle at point K. The measures of JL and JML are 127 and 233 degrees, respectively. How to determine the measures of angles JL and JML? From the complete question, we have: JL = 127 degrees. The sum of angles at a point is 360 degrees. So, we have: JML + 127 = 360. Subtract 127 from both sides. JML = 233

The arc measure is the degree measure of the arc between the two points where the central angle intersects the circle. The arc length is the actual length of the arc itself, and it depends on both the radius of the circle and the degree measure of the arc. The formula is: x . For example, if a central angle of a circle has a measure of 60 ...