Question

Measure Angles Practice

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Question
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The semicircular shape of a protractor is drawn with measurements. Four rays are superimposed on the protractor. The markings on a protractor range from 0 to 180 degrees from left to right on the outer scale. The markings on a protractor range from 0 to 180 degrees from right to left on the inner scale. Radial lines are drawn from the origin at the center of the baseline outward to form the angles marked on both the inner and outer scales. The origin is labeled as B. A ray labeled B A extends from point B along 18 degrees on the outer scale. A second ray labeled B D extends from point B along 57 degrees on the outer scale. A third ray labeled B E extends from point B along 127 degrees on the outer scale. The fourth ray labeled B C extends from point B along 158 degrees on the outer scale. The angles formed by the four rays are marked with arcs.

What is the measure of angle ABC ?

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The measure of angle ABC is 158 degrees.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response. To find the measure of angle ABC, we need to subtract the measure of angle BCD from 180 degrees.

The measure of angle BCD is the difference between the measures of angles ACD and ABD.

Angle ACD is the difference between 127 degrees and 57 degrees, which is 70 degrees.
Angle ABD is the difference between 127 degrees and 18 degrees, which is 109 degrees.

So, angle BCD is 70 degrees - 109 degrees, which is -39 degrees.

To find angle ABC, subtract -39 degrees from 180 degrees:
180 degrees - (-39 degrees) = 180 degrees + 39 degrees = 219 degrees.

Therefore, the measure of angle ABC is 219 degrees.

Answer 4

nope

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the incorrect response again. Let's go through the problem again.

From the given information, we have four rays labeled BA, BD, BE, and BC extending from point B along 18 degrees, 57 degrees, 127 degrees, and 158 degrees on the outer scale, respectively.

To find the measure of angle ABC, we need to subtract the measure of angle ABD (angle BCD) from 180 degrees.

The measure of angle ABD (angle BCD) is the difference between the measures of angles BAD and BCD.

Angle BAD is the difference between 18 degrees and 57 degrees, which is 39 degrees.
Angle BCD is the difference between 158 degrees and 57 degrees, which is 101 degrees.

So, the measure of angle ABD (angle BCD) is 101 degrees - 39 degrees, which is 62 degrees.

Finally, to find the measure of angle ABC, we subtract 62 degrees from 180 degrees:
180 degrees - 62 degrees = 118 degrees.

Therefore, the measure of angle ABC is 118 degrees.