When a Principal, by his or her actions, causes a third party to believe that another person is his or her agent and the third party deals with the supposed agent, this is said to be what type of agency relationship?

Relationship by assumed representation.

Explanation:

A third party believes a principal has an agent acting on his behalf and interests without properly confirming from the principal, this relationship is known as relationship by assumed representation.

First, the third party is not told by the principal that a particular person is his agent and will represent him, he assumes it, probably because he sees both of them together.

The third party fails to explicitly ask the principal if the agent represents his interests and goes ahead to deal with the agent, he is merely transacting based on assumed representation.

It is totally different when the principal explicitly tells the third party that this is his agent who will be representing him.

Agency by estoppel

Explanation:

When agency by estoppel is made reference to; it is simply a situation that takes place in which someone behaves in a way that the other person will then or take it or assume that a third individual or party has the necessary right or authority to act on his stead and then commences doing business with this third party.

That very individual that his or her act made him to do the needful is under normal circumstances very much liable for that agreement.