Two squares and three line segments. What’s the angle α?

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## Solution

The angle α is 45°.

## Visual solution

## Poem

Big brother

An Orwell prophecy

Humans are malleable infinitely

Just stop the pain

Learning

Understanding by doing

And accepting

Human being are nothing

Every year fewer and fewer words

And meanings

Big brother is asking

And you are following

And you are lying

And you are dying

## 2 replies on “Big brother”

The angle alpha is 45°.

ABCD is a square, clockwise with A at the left top. E is some point on BC. EFGC is another square, clockwise with E at left top. BG is joined. DE meets BG at H. CH is joined.

The triangles DCE and BCG are congruent. It gives angle EDC = angle GBC.

Thus quadrilateral BDCH is cyclic.

angle BDC + angle BHC = 180° = angle BHC + angle alpha.

angle BDC = angle alpha = 45°