Question

What common angle do ACE and ACD share?

Answer 1

The answer is the second option, <ACE = <ECA.

This is because C is in the middle of both, so it's referring to the same angle. The other options are all comparing different angles, that aren't congruent, so they're incorrect.

Answer 2

∠ACE≅∠ECA

Explanation:

If we take ΔACE and ΔACD,

∠ACE and ∠ECA are the common angle as compared to the rest one given.

If we take, ∠AFB and ∠EFD, both the angles are not contained in the given triangle.

Similarly, if we take ∠EBC and∠ECB, the ∠EBC is not included in the triangle ACE.

In, ∠CAD and ∠CEB, both the angles cannot be equal.