Tessellate S.T.E.M.S. (2019) - Mathematics - Category A (School) - Set 4 - Objective Problem 4

Geometry Level 3

Given a given convex quadrilateral A B C D ABCD , let I A , I B , I C , I D I_A, I_B, I_C, I_D denote the respective incentres of triangles D A B , A B C , B C D , C D A DAB, ABC, BCD, CDA . Suppose we have ∠ B I A A + I C I A I D = 18 0 ∘ \angle BI_AA + I_CI_AI_D = 180^\circ . Then find the value of ∠ B I B A + I C I B I D \angle BI_BA + I_CI_BI_D .

This problem is a part of Tessellate S.T.E.M.S. (2019)

18 0 ∘ 180^\circ 13 5 ∘ 135^\circ 9 0 ∘ 90^\circ 12 0 ∘ 120^\circ

Tessellate S.T.E.M.S. Mathematics by Tessellate S.T.E.M.S. Ma… , 26

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