Step-by-step explanation:
there are many people that find geometry easier, because here you can actually "touch" something and "see" what we are doing and dealing with.
anyway,
let's just remember what a parallelogram is and represents :
it has 2 pairs of parallel sides (the sides in each pair are parallel to each other). hence the name.
in order for that to be possible the sides in every pair must be equally long. in our case here : FG = EH, FE = GH.
the diagonals cross each other at their midpoints.
and then we see in the graphic how the diagonals split the the whole parallelogram into 4 triangles.
so, now we have all tools to solve the puzzles.
we know, I is the midpoint of both diagonals. and therefore, EI = IG, FI = IH
and that means
3x - 1 = 8
3x = 9
x = 3
the triangles FIG and EIH are congruent. that means, if you turn them to be oriented in the same direction and then place them on top of each other, they would cover each other perfectly.
and that means that they have the same angles and side lengths.
therefore, when we know things about one of these triangles, we know the same things about the other triangle. like the angles.
so, the angle IHE = IFG = 31°
the angle IEH = IGF = 46°
why do we know the 2 triangles are congruent ?
because the 3 sides of FIG are exactly as long as the 3 sides in EIH :
FG = EH
IG = EI
FI = IH
and that satisfies the SSS criteria (side-side-side) for congruent triangles.
and again, therefore, the angles must be the same too.
