AB and CD intersect at point O AO = 12cm BO = 4cm CO = 30cm DO = 10cm angle DOB = 52 degrees

AB and CD intersect at point O AO = 12cm BO = 4cm CO = 30cm DO = 10cm angle DOB = 52 degrees angle DBO = 61 degrees. What is the angle ACO.

The ratio of the lengths of the segments OC / ОD and ОА / ОВ is the same.

OC / OD = 30/10 = 3.

ОА / ОВ = 12/4 = 3.

Angle BOD = AOC as vertical angles.

Then the triangle BOD and AOD are similar in two proportional sides and the angle between them with a similarity factor of 3.

In the triangle OBD, we determine the value of the angle ODB. ОDВ = 180 – DBO – DОВ = 180 – 61 – 52 = 67.

The segments VD and AC, OD and OS are similar sides, then the angle ACO = BDO = 61.

Answer: The ACO angle is 61.