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Arc \(LM\) on circle \(O\) has a measure of \(40^\circ\).

Circle \(O\) is shown. Line segments \(LO\) and \(MO\) are radii. Sector \(LOM\) is shaded.

Which statements are true? Check all that apply.

- The central angle measure created by the shaded region is \(40^\circ\).
- The central angle measure created by the shaded region is \(20^\circ\).
- The ratio of the measure of \(\angle LOM\) to the measure of the whole circle is \(\frac{1}{9}\).
- 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 \(LOM\).

Answer :

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

Circle O can be divided into a total of 10 sectors equal in area to sector LOM.

Based on the given information, we can determine the following:

The central angle measure created by the shaded region is 40°. (True) This is stated in the problem.

The central angle measure created by the shaded region is 20°. (False) The given measure is 40°, not 20°.

The ratio of the measure of ∠LOM to the measure of the whole circle is one-ninth. (False) We cannot determine this ratio without knowing the measure of the whole circle. The given information only provides the measure of arc LM, not the entire circle.

Circle O can be divided into a total of 9 sectors equal in area to sector LOM. (False) Without knowing the measure of the whole circle or the radius, we cannot determine the number of sectors equal in area to sector LOM.

Circle O can be divided into a total of 10 sectors equal in area to sector LOM. (True) Given that the measure of arc LM is 40°, we can divide the circle into 9 equal sectors of 40° each, making sector LOM one of those sectors.

Therefore, the true statements are:The central angle measure created by the shaded region is 40°.

Circle O can be divided into a total of 10 sectors equal in area to sector LOM.

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