Question

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 $\frac{1}{9}$.□ 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.

Explanation:

Step1: Match arc to central angle

The measure of a central angle equals its intercepted arc. Arc LM = $40^\circ$, so $\angle LOM = 40^\circ$.

Step2: Calculate angle-to-circle ratio

Whole circle = $360^\circ$. Ratio: $\frac{40^\circ}{360^\circ} = \frac{1}{9}$.

Step3: Find number of equal sectors

Divide full circle by sector angle: $\frac{360^\circ}{40^\circ} = 9$.

Answer:

• The central angle measure created by the shaded region is $40^\circ$.
• 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.