How is this angle measured in the triangle?Given the image below:Let the angle at vertex A be called α. Polya says by looking at the diagram and the isoceles triangles △ A C E and △ A B D we can deduce that ∠ D A E = α 2 + 90 ° .Where will I get 90 ° from?

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How is this angle measured in the triangle?Given the image below:Let the angle at vertex A be called   α. Polya says by looking at the diagram and the isoceles triangles   △      A    C    E   and   △      A    B    D   we can deduce that   ∠      D    A    E    =      α    2    +  90      °  .Where will I get   90      °   from?

devilvunga · Accepted Answer

Step 1  ∠  D  A  E  =  ∠  E  A  C  +  ∠  D  A  B  +  α  =            180              °            −      ∠      A      C      E        2    +            180              °            −      ∠      A      B      D        2    +  α  =            ∠      A      C      B      +      ∠      A      B      C        2    +  αStep 2  =            180              °            −      α        2    +  α  =  90      °    +      α    2

Hana Buck · Accepted Answer

Step 1Exterior angle of triangle = sum of 2 interior opposite angles  ∠  A  C  B  =  2  ∠  E  A  C    ∠  A  B  C  =  2  ∠  D  A  B  Step 2  ⇒  ∠  E  A  C  +  ∠  D  A  B  =  0.5  (  ∠  A  C  B  +  ∠  A  B  C  )  =  0.5  (  180  −  α  )  ∠  D  A  E  =  90  −  0.5  α  +  α

Let the angle at vertex A be called alpha. Polya says by looking at the diagram and the isoceles triangles triangle ACE and triangle ABD we can deduce that angle DAE=alpha/2+90^circ.

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