What are two angles in a plane which share a common vertex and a common side but do not overlap?

Solution:

Consider two intersecting lines, say, AB and CD intersect at O as shown in the figure.

There are two kinds of angles formed; Vertically opposite angles and adjacent angles.

We have two pairs of vertically opposite angles made by the intersecting lines and these angles do not share a common side. 

(i) ∠AOC and ∠DOB 

(ii) ∠BOC and ∠DOA

We have four pairs of adjacent angles:

(i)∠AOC and ∠BOC share a common side OC at the vertex O

(ii)∠AOD and ∠BOD share a common side OD at the vertex O

(IIi)∠BOC and ∠DOB share a common side OB at the vertex O

(iv)∠AOC and ∠DOA share a common side OA at the vertex O

Thus, required angles are adjacent angles. The two angles in a plane which share a common vertex and a common side but do not overlap are the adjacent angles.

What are two angles in a plane which share a common vertex and a common side but do not overlap?

Summary:

Two angles in a plane that share a common vertex and a common side but do not overlap are the adjacent angles.