What do you mean? What interior angles?
I think this problem is pictured very misleadingly and might even be incomplete.
Triangles ADB and DBC share the side DB. But the line CA does not actually exist as pictured, CA has to be in fact 2 segments that can’t meet in the middle, because of how these segments divide the angles at A and C (by 1/3 ratio and by half respectively).
But then you end up with 2 different triangles, one of them (ADB) iscosceles that have no real solution, unless we had more information relating them, like if AB and DC were parallel, but that is a stretch given the picture misleadingness.
That would make it an isosceles triangle, not an equilateral triangle.
Oh yeah. Fuuuuck 
. It’s not an equilateral triangle
Isosceles is two sides of equal length.
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And two equal angles 
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Seems like I’m the one doing that R.Kelly maths. 
Cos I left school in 1991 and I’m clearly dumb as f@ck
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If you work from x=15°, you will see that it is possible.
From my extremely advanced design software Powerpoint:
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You can see yourself that the middle segment has to be “hit” right in the middle on the right side, but has to be hit above the middle (dividing itself into 1/3 above and 2/3 below) from the left side.
Your drawing does not hold scrutiny!
Let me show you my skills in advance design software Paint
I actually envy your Paint abilities. All I can do is draw ugly stuff with my finger or a stylus on a touchscreen.
This doesn’t make sense
The segment on the left side will be colinear with the right side if there are x degrees above and 2x degrees below the line as in my drawing above.
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Ah, you are right, I’m totally wrong! Let me get back to the drawing board.
Lets replace that one, its confusing.
ABD is 6x + Y, there fore A center line to B is also 4X
Whatever is on the other side of the horizontal line is 180-4X
A centerline D is 4X + (180-4X) therefore C centerline B is essentially the same put 3X by the B
Shorten your DC and you’ll see is possible 
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Why are you calling another angle A?
Or are you suggesting both angles are the same?
angle DAC = angle BCA = x, pair angles like those in line cutting across two parallel lines are called interior angles.
So, are you assuming AB and DC are parallel?
They can’t be.
It’s AD and BC that are.
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