Answer: Since AFGH is a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We can use this property, known as the triangle inequality theorem, to determine the angles of AFGH in order from largest to smallest.
We are given that the perimeter of AFGH is 87, so we know that:
FG + GH + FH = 87
6x + 7 + 8x - 5 + 10x - 11 = 87
24x + 1 = 87
24x = 86
x = 3.5
Now that we know that x = 3.5, we can use the given lengths of the sides to find the values of the sides:
FG = 6x + 7 = 6(3.5) + 7 = 23
GH = 8x - 5 = 8(3.5) - 5 = 25
FH = 10x - 11 = 10(3.5) - 11 = 29
We can now use these values to determine the angles of AFGH in order from largest to smallest.
We can use the triangle inequality theorem to determine that:
FH>FG+GH
29>23+25
Therefore, the angle that is opposite to side FH is the largest angle in the triangle, and the angles opposite to FG and GH are the smaller angles.
So, the angles in the triangle AFGH are ordered from largest to smallest:
The angle opposite to side FH, angle A, is the largest.
The angles opposite to side FG and GH are the smaller angles.
Explanation: