Central Angles and Arc Measures in Circles

This page presents a series of problems focused on central angles and arc measures in circles. Students are tasked with finding arc measures and solving for unknown values in various circle configurations.

Definition: Central angles are angles formed by two radii of a circle, with the vertex at the center of the circle.

Definition: Arc measures refer to the degree measure of a portion of a circle's circumference.

The problems on this page can be categorized into two main types:

1. Finding arc measures given central angles
2. Solving for unknown values (x) in circle problems

Example: In problem 1, students must find mJL, mJML, mCFD, mDFE, and mDE given various angle measures in the circle.

Example: Problem 2 requires solving for x in the equation 31 + 9x + 23 = 180, which relates to the measures of angles in a circle.

Highlight: The page emphasizes the relationship between central angles and their corresponding arc measures, a fundamental concept in circle geometry.

Vocabulary: Bisect - to divide into two equal parts. This term is used in problem 10, where CH bisects ∠DHG.

The problems increase in complexity throughout the page, building on students' understanding of central angles and arc measures in circles.