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Here we go again. Tired of these yet? Obtuse triangles.

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The sum of interior angles in an obtuse triangle is 180°.
I'm pretty sure I have gotten this down. 180° - 84° = solution.

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Other answers:

well the 2 curved arcs that make DGF also make DEF.. so I'd say the angles are equal... and in a kite those angles are equal...
oh and the triangle DGF is reflected in the line DF to form DEF...
With the answers provided, "none of the above" would be equal to 96°, yes?
the angles DEF and DGF are not supplementary... which is what you have done... they are congruent
\[\angle DGF ≅ \angle DEF \] by ASA method?
but I don't think you need to prove congruency... just recognise the equal angle markings..
84° is equal to 84°.

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