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.
Answer:
actually it was 29 degrees
Step-by-step explanation:
my homework said so!
