Answer:
[tex]\huge\boxed{x=20}[/tex]
[tex]\huge\boxed{H = 58, I = 71, J = 51}[/tex]
Step-by-step explanation:
In order to find the measure of our angle, we have to note angle relationships.
All angles in a triangle will add up to 180°
This means all the angles in this triangle will equal 180, or:
[tex](4x - 9) + (3x - 2) + (3x-9) = 180[/tex]
We can simplify this equation down to find the value of x.
Combine like terms:
[tex]10x - 20 = 180[/tex]
Add 20 to both sides:
[tex]10x = 200[/tex]
Divide both sides by 10:
[tex]x = 20[/tex]
Now that we know the value of x, we can substitute it into the equation for each angle to find it's value.
m∠H:
[tex]3x-2\\3(20)-2\\60-2\\\\58[/tex]
m∠I
[tex]4x-9\\4(20)-9\\80-9\\\\71[/tex]
m∠J
[tex]3x-9\\3(20)-9\\60-9\\\\51[/tex]
To further prove this is right, we would know that all the angles add up to 180°.
[tex]51+71+58=180[/tex], so we should be right.
Hope this helped!
