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

Question

Here we go again. Tired of these yet? Obtuse triangles. <DGF = 84°, then <DEF = ?°

42°
84°
48°
none of these

lime · Answer

attachment

lime · Answer

The sum of interior angles in an obtuse triangle is 180°.

lime · Answer

I'm pretty sure I have gotten this down. 180° - 84° = solution.

campbell_st · Answer

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...

campbell_st · Answer

oh and the triangle DGF is reflected in the line DF to form DEF...

lime · Answer

With the answers provided, "none of the above" would be equal to 96°, yes?

campbell_st · Answer

the angles DEF and DGF are not supplementary... which is what you have done... they are congruent

lime · Answer

$$\angle DGF ≅ \angle DEF $$
by ASA method?

campbell_st · Answer

but I don't think you need to prove congruency... just recognise the equal angle markings..

lime · Answer

84° is equal to 84°.

campbell_st · Answer

correct