Question

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

Circle O is shown. Line segments L O and M O are radii. Sector L O M is shaded.

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 One-ninth.
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 1

The statements that are true are;

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 One-ninth.  

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

What is the central angle?

A central angle can be defined as an angle whose vertex is the center O of a circle and whose radii intersecting the circle in two distinct points

Note that;

The two radii are L O and MO

The measure of the angle is 40°

The sector is LOM

From the information given, it can be deduced that the 2 radii that forms the central angle is depicted by the shaded region which is said to have an angle of 40°. The sum of Circle O is one that can be shared into  9 equal sectors and that can be also equal in area to sector that is marked LOM

It can also be deduced that the circle can be divided into 9 equal sectors.

Thus, the statements that are true are;

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 One-ninth.  

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

Learn more about a circle here:

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