In circle o, the length of radius ol is 6 cm and the length of arc lm is 6.3 cm. the measure of angle mon is 75°. rounded to the nearest tenth of a centimeter, what is the length of arc lmn? 7.9 cm 10.2 cm 12.6 cm 14.2 cm

You need to start by finding the length of arc MN.
 
To do this, find the circumference of the circle. This is given by 2*pi*r. The radius is 6 cm, so 2r=12. pi*12 is approximately 37.68.

Next, you need to find the fraction of the circle made up by the sector MON. Since angle MON is 75 degrees, and the whole circle is 360 degrees, MON makes up 75/360 of the circle.

This means that arc MN makes up 75/360 of the circumference. 
(75/360)*(37.68)=7.85.

Finally, add the arc length LM, which is 6.8.
6.3+7.85=14.15

Rounded to the nearest tenth of a centimeter, this is 14.2 cm. 

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