Interior and Exterior Triangle Angles

Question

In ΔGHI, \overline{GI} GI is extended through point I to point J, \text{m}\angle IGH = (x+16)^{\circ}m∠IGH=(x+16) ∘ , \text{m}\angle HIJ = (4x-12)^{\circ}m∠HIJ=(4x−12) ∘ , and \text{m}\angle GHI = (x+10)^{\circ}m∠GHI=(x+10) ∘ . Find \text{m}\angle GHI.m∠GHI.

Answer 1

In a triangle the measure of an exterior angle is equal to the sum of the measures of the two remote angles. Theorem.

4x - 12 = (x + 16) + (x + 10)