In ΔGHI, \overline{GI} GI is extended through point I to point J, m∠GHI = (x+10)^{\circ}(x+10) ∘ , m∠IGH = (x+12)^{\circ}(x+12) ∘ , and m∠HIJ = (4x-6)^{\circ}(4x−6) ∘ . Find m∠GHI.

Answer 1

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

So, ∠GHI+∠IGH=∠HIJ 

x+10+x+12=4x-6

x=14

∠GHI=x+10=24