Explanation:
the table was filled correctly already by somebody yesterday.
the important thing to remember is that an arc angle is always measured at the center point of the circle. that is the difference to angles between the intersecting lines of arc segments.
it would be really important that you start doing these things yourself. this hands-on experience of these (really basic) questions is designed to help you get a feeling how these things work together, which makes later topics much easier for you.
please tell me what you don't understand here. you only need to apply common sense. no magic voodoo math formulas or strategies.
FAR = 100° FR = 140° VO = 60° FR+VO = 200°
FAV = 80° FV = 60° RO = 100° FV+RO = 160°
OAV = 100° VO = 60° FR = 140° VO+FR = 200°
OAR = 80° RO = 100° FV = 60° RO+FV = 160°
how did we get the measures of the intercepted arcs ? by counting the 20° segments on the arc. the full circle arc represents 360°. always, for every circle. one time around is one time around and therefore 360°, no matter the size of the circle.
when you stand directly on the south pole of the Earth for 24 hours, you will have rotated the full 360° in that time (one rotation per day). if you stand on the equator for 24 hours, the Earth has taken you on one spin of the full 360°. the difference is the absolute arc length and the necessary speed at which we cover the distance of a full arc length.
every 250 million years our whole sogar system rotates once (by the full 360°) around the center of our galaxy.
the degrees have nothing to do with radius, diameter, area, ... of a circle. only with the relative parts of the circumference. when the minute arm of a clock moved for 15 minutes, then it went 90° around the clock's face. after 60 minutes it went the full 360°, and the cycle starts anew.
so, minutes on a clock or hours of the day are just another way of counting degrees around a circle.
what have we noticed with the sum of the measures of the intercepted arcs ?
many things.
e.g.
they are exactly twice as large as the line angles. 100 to 200. 80 to 160.
the sum of 2 pairs of opposing arc angles is always 360°.
...
so, how will we get the line angles based on the sum of the angles of the intersected arcs ?
we cut the sum of the intersected arc angles in half. 200 to 100. 160 to 80.