AB and CD meet at point O, AO = 12 cm, BO = 4 cm CO = 30 cm DO = 10 cm

AB and CD meet at point O, AO = 12 cm, BO = 4 cm CO = 30 cm DO = 10 cm DOB angle = 52 degrees DBO angle = 61 degrees Find ACO angle

Let us find the ratio of the segments OB / OD of the triangle OBD and OA / OS of the triangle OAS.

ОВ / ОD = 4/10 = 2/5.

OA / OC = 12/30 = 2/5.

Since the ratio of the sides is equal, the sides are proportional.

Angle AOC = BOD as vertical angles at the intersection of segments AB and CD.

Then the triangles AOC and BOD are similar in two proportional sides and the angle between them.

Then the angle ОАС = ОDВ = (180 – DОВ – DВО) = (180 – 52 – 61) = 67.

Answer: The angle OAC is 67.