Question

12. Critique Reasoning Camille describes how to solve the problem to the right by writing the following: Divide the measure of ZDBE by 2. This will give the measure of the intercepted arc. Explain the error in Camille's thinking. Then show the correct steps for solving and the correct answer. Given the diagram below, find mDE. A B 48° с E 40° D​

Answer 1

Camille's reasoning is flawed as she assumes the intercepted arc is a semicircle. To find the correct measure of arc DE, determine the central angle (DBE = 88°) and divide it by 2, yielding a correct measure of 44°.

Critique of Camille's reasoning:

Camille's reasoning is incorrect because she assumes that the intercepted arc is a semicircle. However, this is not necessarily the case. The intercepted arc can be any size, as long as it is centered on the central angle.

Correct steps for solving the problem:

To find the measure of the intercepted arc DE, we can use the following steps:

1. Find the measure of the central angle DBE.

2. Divide the measure of the central angle by 2.

3. The result is the measure of the intercepted arc DE.

From the diagram, we can see that the measure of the central angle DBE is 40° + 48° = 88°.

Therefore, the measure of the intercepted arc DE is 88° / 2 = 44°.

The measure of the intercepted arc DE is 44°.