Problem
In triangle BDC the angles add to 180 degrees, so the apex angle at D is 180 - 40 - 80 = 60 degrees.
Grade 4 students know the three angles of a triangle always total 180 degrees.
4.MD.C.7Identify SubproblemsBE = DE makes triangle BED isosceles (base angles 40°): angle DEB = 100°, so angle DEC = 180 - 100 = 80 degrees (B, E, C collinear).
Equal sides give equal base angles, and angles on a straight line add to 180 degrees.
4.MD.C.7Identify SubproblemsFolding brings ED down onto EC, halving angle DEC: angle FEC = 80 ÷ 2 = 40 degrees; angle FCE stays angle C's 80 degrees.
A folded shape lies exactly on top of its original, so matching angles stay the same size.
4.MD.C.7Create A Physical RepresentationFolding the apex flap down along the crease at E brings a 40-degree angle onto E, so angle FEC measures 40 degrees.
A fold lays one layer of paper exactly on top of another, so the angle that arrives at E after folding stays the same size as the angle that was folded over.
The angle that gets folded over measures 40 degrees, because it is a base angle of the isosceles triangle BED, whose equal sides BE and DE force its two base angles to match the 40-degree angle already at B.
Since BE and DE are equal, triangle BED can be folded along its middle so one base angle lands exactly on top of the other, which shows the two base angles are equal.
In triangle EFC the three angles add to 180 degrees: angle EFC = 180 - 80 - 40 = 60 degrees.
Once two angles of a triangle are known, the third comes from the 180-degree total.
4.MD.C.7Identify SubproblemsThis only needs Grade 4 angle-adding and the fact that folded angles stay equal!