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all plane angles at vertex A are equal, triangular pyramid

Source: IV Soros Olympiad 1997-98 R3 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024
geometryangle bisector3D geometrypyramid

Problem Statement

At the base of the triangular pyramid ABCDABCD lies a regular triangle ABCABC such that AD=BCAD = BC. All plane angles at vertex BB are equal to each other. What might these angles be equal to?
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