If the figures shown are congruent, what is the value of x? (hint: the sum of the three angles of any triangle is 180°.)
38°
100°

42°
100
38°
80°

THIRD OPTION.

Step-by-step explanation:

For this exercise it is important to remember that, by definition, two triangles are congruent when all their corresponding sides and their corresponding angles are congruent.

Therefore, the size and shape of two congruent triangles are equal.

In this case you know that the triangles shown in the given picture are congruent.

So, based on the explained before, you know that the measure of every corresponding angle of both triangles is the same.

Then, you can conclude that unknown angle "x" has the same measure that the corresponding angle of the other triangle:  .

Therefore, you get that the value of "x" is:

This matches with the third option.

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh

i believe so, according to my "strange" way of figuring out weird math problems like this.