In ΔGHI, \overline{GI} GI is extended through point I to point J, \text{m}\angle GHI = (3x+13)^{\circ}m∠GHI=(3x+13) ∘ , \text{m}\angle IGH = (x+8)^{\circ}m∠IGH=(x+8) ∘ , and \text{m}\angle HIJ = (6x-5)^{\circ}m∠HIJ=(6x−5) ∘ . Find \text{m}\angle GHI.m∠GHI.

Given:

In ΔGHI, GI is extended through point I to point J.

[tex]m\angle GHI=(3x+13)^\circ,m\angle IGH=(x+8)^\circ,m\angle HIJ=(6x-5)^\circ[/tex]

To find:

The measure of angle GHI.

Step-by-step explanation:

According to exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of measure of two opposite angles.

Using exterior angle theorem, we get

[tex]m\angle HIJ= m\angle GHI+m\angle IGH[/tex]

[tex](6x-5)^\circ=(3x+13)^\circ+(x+8)^\circ[/tex]

[tex](6x-5)^\circ=(4x+21)^\circ[/tex]

[tex]6x-4x=21+5[/tex]

[tex]2x=26[/tex]

Divide both sides by 2.

[tex]x=13[/tex]

Now,

[tex]m\angle GHI=(3x+13)^\circ[/tex]

[tex]m\angle GHI=(3(13)+13)^\circ[/tex]

[tex]m\angle GHI=(39+13)^\circ[/tex]

[tex]m\angle GHI=52^\circ[/tex]

Therefore, the measure of angle GHI is 52 degrees.

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