​O is the centre of the circle . If ang. DAO =48degree   ang. DCO =31 degree .what is the measure of ang .AOC​

join DO.
in triangle, oad,     oa = od                               ( radius )
therefore => angle oad = angle oda = 48      ( angles opposite to equal sides are equal)
in triangle ocd,     oc = od                                ​( radius )
=> angle ocd = angle odc = 31                        ​( angles opposite to equal sides are equal)
angle adc = angle oda + angle odc
= 48 + 31
= 79 degrees
NOW, angle aoc = 2 x angle adc                    (central angle theorem, angle at centre is 2 times angle at any point on the circle)
therefore angle aoc = 2 x 79 = 158 degrees
THUMBS UP PLZZZ !!