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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.

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Given:

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


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

To find:

The measure of angle GHI.

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


m\angle HIJ= m\angle GHI+m\angle IGH


(6x-5)^\circ=(3x+13)^\circ+(x+8)^\circ


(6x-5)^\circ=(4x+21)^\circ


6x-4x=21+5


2x=26

Divide both sides by 2.


x=13

Now,


m\angle GHI=(3x+13)^\circ


m\angle GHI=(3(13)+13)^\circ


m\angle GHI=(39+13)^\circ


m\angle GHI=52^\circ

Therefore, the measure of angle GHI is 52 degrees.

In ΔGHI, \overline{GI} GI is extended through point I to point J, \text{m}\angle GHI-example-1
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