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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Name and Measure the Major Arc

Master Arc Measurements with Engaging Practice Problems

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Major Arc Mastery, a geometry practice quiz for high school students.

In a circle, if a minor arc AB measures 140°, what is the measure of the corresponding major arc ACB?
220°
140°
180°
200°
The major arc is found by subtracting the measure of the minor arc from the total circle measure. Since the circle measures 360°, 360° - 140° gives 220°.
What defines a major arc in a circle?
An arc that measures more than 180°
An arc that measures exactly 180°
An arc that measures less than 180°
An arc that measures 90°
A major arc is defined as an arc whose measure is greater than 180°. An arc of exactly 180° is called a semicircle, and arcs less than 180° are minor arcs.
If a central angle measures 30° in a circle, what is the measure of the intercepted major arc?
330°
30°
150°
180°
The intercepted minor arc has the same measure as the central angle. For the major arc, subtract the minor arc from 360°. Thus, 360° - 30° equals 330°.
If a minor arc in a circle is 160°, what is the measure of its major arc?
200°
160°
180°
220°
The major arc is calculated by subtracting the measure of the minor arc from 360°. Therefore, 360° - 160° equals 200°.
Which statement correctly describes a major arc?
It is larger than a semicircle (greater than 180°)
It is exactly half of a circle (180°)
It is less than 90°
It is always equal to its central angle
A major arc is one that measures more than 180°, which makes it larger than a semicircle. The other options do not match the definition of a major arc.
In circle O, minor arc EF measures 100°. What is the measure of the corresponding major arc EGF?
260°
100°
280°
200°
Subtract the measure of the minor arc from 360° to find the major arc. Thus, 360° - 100° equals 260°.
In a circle, chord BC subtends a minor arc of 75°. What is the measure of the major arc BDC?
285°
75°
150°
195°
The major arc is the remaining portion of the circle when the minor arc is removed. Therefore, 360° - 75° equals 285°.
An inscribed angle intercepts a major arc that measures 280°. What is the measure of the inscribed angle?
140°
280°
70°
110°
An inscribed angle measures half the intercepted arc. Half of 280° is 140°.
If a central angle in a circle is 45°, what is the measure of the intercepted major arc?
315°
45°
135°
180°
The intercepted major arc is the complement of the central angle to 360°. Hence, 360° - 45° equals 315°.
A chord of a circle subtends a central angle of 120°. What is the measure of the major arc opposite this chord?
240°
120°
180°
300°
Subtracting the 120° minor arc (which equals the central angle) from 360° gives 240° for the major arc.
If the major arc ABC of a circle measures 250°, what is the measure of the minor arc AC?
110°
250°
130°
180°
Since the entire circle measures 360°, subtracting the major arc's 250° leaves a minor arc of 110°.
In a circle, a chord subtends a 70° central angle. What is the measure of the corresponding major arc?
290°
70°
140°
210°
The major arc is found by subtracting the 70° minor arc from 360°. This results in 360° - 70° = 290°.
Is an arc measuring 330° considered a major arc?
Yes, because 330° is greater than 180°
No, it must be less than 180°
Only if it is a semicircle
No, arcs are always less than 360°
By definition, a major arc is one that measures more than 180° but less than 360°. Since 330° meets this criterion, it is a major arc.
Consider an arc XY that measures 200°. Which of the following statements is true?
It is a major arc because its measure exceeds 180°
It is a minor arc
It is a semicircular arc
Its measure must be 160°
An arc measuring more than 180° is classified as a major arc. Since 200° is greater than 180°, the statement is true.
In a circle, if a minor arc DE measures 110°, what is the measure of its corresponding major arc?
250°
110°
180°
270°
The measure of the major arc is the remainder when the minor arc is subtracted from 360°. Thus, 360° - 110° equals 250°.
An inscribed angle in a circle measures 120° and intercepts a major arc. What is the measure of the intercepted arc?
240°
120°
240° is not possible
300°
The intercepted arc is twice the inscribed angle. Doubling 120° gives 240°, which qualifies as a major arc since it is greater than 180°.
In a circle, if arc PQ measures 155°, what is the measure of the major arc that complements it (arc PRQ)?
205°
155°
215°
180°
The major arc is the complement of arc PQ to the full circle. Hence, 360° - 155° equals 205°.
Chords AB and AC in a circle form an intercepted arc BC that measures 80°. What is the measure of the corresponding major arc BDC?
280°
80°
200°
300°
Subtracting the intercepted minor arc (80°) from 360° gives the measure of the major arc: 360° - 80° equals 280°.
In a circle, if arc AB represents 25% of the circumference, what is the measure of the corresponding major arc ACB?
270°
90°
180°
300°
25% of a 360° circle is 90°. The major arc is the rest of the circle, so subtract 90° from 360° to get 270°.
If the measure of a minor arc corresponding to a central angle is x degrees, express the measure of the corresponding major arc in terms of x.
360 - x
180 - x
x - 360
360 + x
A full circle measures 360°. The major arc is the difference between 360° and the measure of the given minor arc, so it is expressed as 360 - x.
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Study Outcomes

  1. Identify the major arc in a circle by distinguishing it from minor arcs.
  2. Calculate the measure of a major arc using circle geometry principles.
  3. Analyze the relationship between central angles and their intercepted arcs.
  4. Apply dynamic geometry strategies to solve arc measurement problems.
  5. Interpret geometric diagrams to determine arc classifications correctly.

Quiz: Name & Measure the Major Arc Cheat Sheet

  1. What Is a Major Arc? - A major arc is the "long way" around the circle when you connect two points, taking up more than half of the circumference. Think of it as the scenic route - always over 180 degrees! Arc Circle Basics
  2. Calculating Arc Measure - To find a major arc's measure, subtract the corresponding minor arc from 360°. It's an easy "behind‑the‑scenes" trick that saves you from guessing! Arc Circle Basics
  3. Major + Minor = 360° - No matter which two points you pick, the big arc and the small arc always add up to a full circle: 360 degrees. This is your golden rule for checking work and spotting mistakes! Arc Circle Basics
  4. Spotting Major Arcs - Grab some circle diagrams and practice shading the larger arc. The more you identify them, the faster you'll be on quizzes and exams! Arc Circle Basics
  5. Arc Notation - Major arcs use three points, like arc ABC, with the middle letter marking the "hidden" point you pass through. This notation keeps your work neat and crystal clear. Arc Circle Basics
  6. Central Angles and Arcs - The measure of any major arc matches the size of its central angle. Picture the angle at the center "opening" the circle - what it intercepts is your arc! Arc Circle Basics
  7. Arc Length Formula - Want the actual length of that curve? Use Arc Length = (θ/360) × 2πr, where θ is in degrees and r is the radius. It's your ticket to real‑world measurements! Revision Maths: Circles & Sectors
  8. Degrees vs. Radians - Sometimes angles come in radians instead of degrees (π radians = 180°). Practice toggling between the two for maximum flexibility when solving problems! One Mathematical Cat: Arc Length
  9. Real‑World Uses - Engineers design gears and architects plan domes using major arcs every day. Spot these arcs in bridges, wheels, and fancy stadium roofs for some inspiration! Arc Circle Basics
  10. Review & Practice - Work through sample problems and timed quizzes to build speed and confidence. The more arcs you master now, the smoother your exams will go! Arc Circle Basics
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