Math Problem Statement

Name the minor arc and the major arc.

A circle with center C, has three points E, F, and G marked on the circle. Angle E C F is labeled 68 degrees.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Minor arc: $EF$

Major arc: $EGF$

$EGECFECFECG$ Question 2 Find the measure of the minor arc and the major arc. The measure of the minor arc is $\degree$ .

The measure of the major arc is $\degree$ .

Solution

Question 1:

  • Minor arc: EFEF
  • Major arc: EGFEGF

Question 2:

To find the measures of the minor and major arcs:

  • The measure of the minor arc EFEF is equal to the measure of the central angle ∠ECF\angle ECF, which is 68°.
  • The measure of the major arc EGFEGF is the remaining part of the circle. Since a full circle measures 360°, we subtract the minor arc's measure:
    360∘−68∘=292∘360^\circ - 68^\circ = 292^\circ

Final Answers:

  • Minor arc: 68∘68^\circ
  • Major arc: 292∘292^\circ

Would you like more details on this, or do you have any questions?

Related Questions:

  1. How do central angles relate to the arcs they intercept?
  2. What is the difference between a minor arc and a major arc?
  3. How do you calculate the measure of an arc without the central angle?
  4. Can an arc measure be more than 360°? Why or why not?
  5. How does the concept of arc length differ from arc measure in degrees?

Tip:
Always remember that the sum of the measures of the minor and major arcs between the same two points is 360∘360^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Geometry
Arcs and Angles

Formulas

Sum of angles in a circle = 360°
Measure of major arc = 360° - minor arc

Theorems

Central Angle Theorem
Arc Length and Measure

Suitable Grade Level

Grades 6-8

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