Problem 101. Equilateral Triangle, Pythagoras, Angles.
High School, College

In the diagram below, given an
equilateral triangle ABC, D is an interior point. If
a^{2} = b^{2} +c^{2} prove that the measure of angle BDC is
equal to 150°.
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HINTS:

Pythagorean Theorem Converse

Congruence of Triangles SAS

The sum of the measures of the
three angles of a triangle is
180.