Equal sides force equal base angles

Reading the picture carefully is the whole first step: once you notice that each small triangle has two of the three equal segments as its sides, three isosceles triangles appear where before there was just a tangle of lines.

Fold an isosceles triangle in half and the two equal sides land on each other, carrying the two base angles onto each other too — so equal sides always force equal base angles.

The same fold argument runs a second time; nothing new has to be learned, the known 40° just gets copied across to the other end of the base.

Even though ① is still unknown, knowing that it appears twice is useful information — an unknown that shows up twice is much easier to pin down than one that shows up once.

Angle measure just adds up: two angles sitting side by side at the same corner make one bigger angle whose size is the sum, so the six little pieces regroup into the three corners of triangle ABC.

Because every known angle showed up exactly twice, the whole 180° splits into two equal halves of 90° — so the single unknown is trapped by one subtraction and one halving, no algebra machinery needed.