Angle
Geometry
Level
3
In triangle ABC, AB=AC, and points D and E are on AB and AC respectively such that BD=DE and DE is perpendicular to AC. Compute the angle EBC.
The answer is 45.
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simply take angle BEC = a so, DEB=DBE = 90 - a (because BD = DE) now take EBC = b so, ABC = 90 - a + b = ACB (ABC isosceles). in triangle BEC a + b + 90 - a + b = 180 2b + 90 = 180 b = 45