The answer is 2:1.
The centroid separates the median, or the point from the midpoint of a side of a triangle with its opposite angle, at a ratio of 2:1, meaning that one segment is 1/3 the length of the median and the other segment is 2/3 the length of the median.
Step-by-step explanation:
the angle CDB is the supplementary angle to 9x+10 (angle ADC).
that means they stand together for 180°. as all angles around a single point on one side of a line are together always 180°.
and then, the sum of all angles in a triangle is always 180°.
so,
CDB + (4x + 10) + 50 = 180
CDB = 180 - (9x + 10) = 180 - 9x - 19 = 170 - 9x
therefore,
(170 - 9x) + (4x + 10) + 50 = 180
170 - 9x + 4x + 10 + 50 = 180
-5x = -50
5x = 50
x = 10
angle CDB = 170 - 9x = 170 - 90 = 80°
Oh my. ALEKS brings back terrible memories, but I hope you managed to do this. You should’ve drawn a line splitting the angle perfect in two. I’m not exactly certain how to use the tool as I’ve never really gotten to to that topic, but I hope you did well. :)