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Arc LM on circle O has a measure of 40°.

Which statements are true? Check all that apply.
The central angle measure created by the shaded region is 40°.
The central angle measure created by the shaded region is 20°.
The ratio of the measure of ∠LOM to the measure of the whole circle is .
Circle O can be divided into a total of 9 sectors equal in area to sector LOM.
Circle O can be divided into a total of 10 sectors equal in area to sector LOM.

2 Answers

5 votes

Final answer:

The true statements are: the central angle created by arc LM is 40°; the ratio of the angle to the circle's total measure is 1/9; Circle O can be divided into 9 equal sectors based on arc LM's measure.

Step-by-step explanation:

If arc LM on circle O has a measure of 40°, let's evaluate the true statements about central angle measures and sector areas.

The relationship between an arc and the central angle of a circle is direct, meaning that the angle measure is equal to the arc it intercepts. Therefore, the central angle measure created by the shaded region is 40°, because it corresponds with the arc LM.

As a full circle is 360°, dividing the central angle measure by the full circle's measure gives a ratio of the angle to the whole circle. Therefore, the ratio of the measure of ∠LOM to the measure of the full circle would be 40/360, which simplifies to 1/9.

Regarding the division of the circle into sectors of equal area, since 360° divided by 40° is 9, circle O can indeed be divided into a total of 9 sectors equal in area to sector LOM. It is not possible to evenly divide the circle into 10 sectors of 40° since 10 sectors would each require an angle of 36°.

Based on these considerations, we can confirm the following statements as true:

The central angle measure created by the shaded region is 40°.

The ratio of the measure of ∠LOM to the measure of the whole circle is 1/9.

Circle O can be divided into a total of 9 sectors equal in area to sector LOM.

User Adam Ullman
by
7.7k points
3 votes

Answer:

1,3,4

Step-by-step explanation:

User Bishal Das
by
8.2k points
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