Answer:
m < I = 44, m<G = 44, m<H = 77
Explanation:
So triangle GHI is an isosceles triangle, meaning that the base angles theorem is applicable, (which states that the angles on either side of the base are congruent).
Knowing this, then;
m<I = m<G = 3x + 39
as given, m<H is 4x + 52,
as one knows, the sum of the angles in a triangle is 180 degrees so that means that;
m<I + m<G + m<H = 180
substitute,
3x + 39 + 3x + 39 + 4x + 52 = 180
combine like terms,
10x + 130 = 180
now use inverse operations,
10x = 50
x = 5
so just substitute the answer back in to find the angles.
m<I = 3x + 39
x = 5
3 * 5 + 39
= 15 + 39
= 44
m<I = m<G = 44
m<H = 4x + 52
x = 5
4 * 5 + 52
= 20 + 52
= 72