Answer:
G: 55
H: 70
I: 55
Step-by-step explanation:
We can see that sides IG and HG are congruent, so both angles will be as well. We know that 5x-20 is equal to 3x+10. Because of this, we can start by adding 20 to both equations.
5x - 20 + 20 = 5x
3x + 10 + 20 = 3x + 30
So, we now know that 5x is equal to 3x + 30.
We know that 2x is the difference between 5x and 3x, so we can divide 30 by 2 to find x.
30 / 2 = 15
x = 15
Now, we can use the solved variable to finish the angle measures.
3*15 + 10 = 55
5 * 15 - 20 = 55
So, both I and G are 55 degrees.
Now, we know a triangle has an interior angle sum of 180. So, if we take 180 - 55 - 55, the answer will be H.
55 + 55 = 110
180 - 110 = 70
H = 70