Question

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.

Answer 1

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.