Question

I need help. Thank KB

Answer 1

`\huge\boxed{x=20}`

`\huge\boxed{H = 58, I = 71, J = 51}`

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:

`(4x - 9) + (3x - 2) + (3x-9) = 180`

We can simplify this equation down to find the value of x.

Combine like terms:

`10x - 20 = 180`

Add 20 to both sides:

`10x = 200`

Divide both sides by 10:

`x = 20`

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:

`3x-2\\3(20)-2\\60-2\\\\58`

m∠I

`4x-9\\4(20)-9\\80-9\\\\71`

m∠J

`3x-9\\3(20)-9\\60-9\\\\51`

To further prove this is right, we would know that all the angles add up to 180°.

`51+71+58=180`, so we should be right.

Hope this helped!