Given the figure, prove that ∠CAK > ∠G

Question

Answer 1

This is a great question! Something that may help you in proving that ∠CAK > ∠G is considering pairs of vertical angles and supplementary angles (such as ∠GBA and ∠CBA; ∠CHG and ∠AHG; and ∠CAB and ∠CAK). It will also be helpful to look at triangles like triangle CHG and triangle CAB. Remember that the sum of all interior angles of a triangle is always 180 degrees. Does that help?

Answer 2

Using the Exterior Angle Theorem:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠CAK = ∠C + ∠G

Since ∠C >0 and ∠G > 0

Therefore ∠CAK > ∠G