Distance 64804

Dan is the square ABCD. At its diagonal AC lies point E. The distance AB is equal to the distance AE. What is the size of the EBC angle?

Correct answer:

EBC =  22.5 °

Step-by-step explanation:

$$\begin{gathered} |AE|=|AB|=a \\ \angle EAB=90/2=45{}^{\circ } \\ \Delta EAB:a-a-x \\ \angle AEB=(180-\angle EAB)/2=(180-45)/2=\frac{135}{2}=67.5{}^{\circ } \\ \angle ABE=\angle AEB=67.5=\frac{135}{2}=67.5{}^{\circ } \\ EBC=\angle EBC=90-\angle ABE=90-67.5=22.5^{\circ }=22°30^{\prime } \end{gathered}$$

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