Problem
The three angles fill the 180-degree straight line, so BOC plus COD is the part left after the 40-degree angle.
A flat line is 180 degrees; remove the known piece and the other two pieces share the rest.
4.MD.C.7Identify SubproblemsSet aside the extra 30 from 140 - the rest splits into two equal COD-sized parts.
Two parts differ by 30; take the extra away so they match, share equally, and that equal part is the smaller angle.
4.MD.C.7Guess And CheckTaking the extra 30-degree difference out of the 140-degree total and then halving what remains gives the measure of angle COD.
The larger angle BOC is just angle COD with 30 more added on, so the 140-degree total is one COD-sized part plus another COD-sized part plus an extra 30.
Angle BOC breaks into a piece exactly the size of COD and a separate 30-degree piece, and those two pieces add back together to remake BOC.
With BOC written as COD-and-30, the total reads COD plus 30 plus COD, and the addends can be reordered so the two equal CODs sit together and the 30 stands apart.
Subtracting that extra 30 back off the 140 leaves exactly the two equal COD-sized parts, because taking away undoes the adding that put the 30 there.
Splitting that leftover evenly between the two equal parts gives the size of a single COD, because dividing by two reverses doubling it.
Take the known angle off the 180-degree line, set aside the extra 30, then share what is left in two - all Grade 4 angle adding and subtracting!