Problem
Because AM = AD, triangle AMD is isosceles with apex A, so its two base angles, angle AMD (at M) and angle ADM (at D), are equal.
Two equal sides always sit opposite two equal angles, so the corners at M and D in this triangle match.
4.G.A.2Draw A DiagramIn triangle AMD the two base angles, the one at M and the one at D, are equal.
The two sides meeting at the top vertex A, sides AM and AD, are the same length, so the triangle looks the same on both sides of the line running straight down from A.
Fold the triangle along that line from A: the equal side AM lands exactly on side AD, which carries the corner at M right onto the corner at D, so those two base angles match.
The base angle at M is given as 40 deg, so the base angle at D inside the triangle is also 40 deg.
Once one base angle of an isosceles triangle is known, the other base angle is the same number.
4.MD.C.6Identify SubproblemsThe three angles of triangle AMD add to 180 deg, so the apex angle a at A is 180 − 40 − 40 = 100 deg.
After taking away the two equal base angles, the leftover of 180 deg is the top angle at A.
4.MD.C.7Identify SubproblemsEqual sides mean equal base angles, so two 40 deg corners leave a 100 deg angle at A: just the triangle's leftover of 180 deg!