A certain graph contains 21 edges and 7 vertices Degree of V

A certain graph contains 21 edges and 7 vertices. Degree of Vertex L = 8, Degree of Vertex M = 5, Degree of Vertex N = 9, Degree of Vertex O = 8, Degree of Vertex P = 4, Degree of Vertex Q = 4 Degree of Vertex R be? What must the degree of vertex R be? There is only one correct answer.

Solution

sum of the degrees of the vertices is twice the number of edges

Degree of vertex L + Degree of Vertex O+Degree of VertexR+Degree of Vertex P+Degree of Vertex Q+Degree of Vertex M+Degree of Vertex N=2*21

8+8+Degree of Vertex R+4+4+5+9=42

Degree of Vertex R+38=42

Degree of Vertex R=4