Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why abc lmn?

D, E, and F

Step-by-step explanation:

D.  SAS can be used, side-angle-side.  The angle is the right angle in both and right angles always are congruent since they can only measure 90 degrees.  The heights of both triangles are marked with the same number of slashes, so they are congruent; likewise, the bases are marked with the same number of slashes, so they are congruent.  Since the angle is between the sides, or included, this is SAS.

E.  HL can also be used since the hypotenuses of both triangles are marked with the same number of slashes, they are congruent.  We already decided the legs of both were congruent to each other.

F.  LL (which is also exactly the same as SAS) can also be used since we already decided that the legs in both triangles are congruent.

HL

Step-by-step explanation:

We have to find which congruence theorem or postulates could be reasons for

In triangle ABC and triangle LMN

Therefore,

Reason: HL

When two right angles in which one  leg and hypotenuse of one triangle is equal to corresponding leg and hypotenuse of other triangle.Then , the triangles are congruent by HL postulates.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°