Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Given that (i) face = 7, vertices = 10, edge = x

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ 7 + 10 = x + 2

⟹ 17 = x + 2

⟹ X = 17-2

⟹ X = 15.

Given that (ii) face = y, vertices = 12, edge = 18

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ y + 12 = 18 + 2

⟹ y + 12 = 20

⟹ y = 20-12

⟹ y = 8

Given that (iii) face = 9, vertices = z, edge = 16

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ 9 + z = 16 + 2

⟹ 9 + z = 18

⟹ Z = 18-9

⟹ Z = 9.

Given that (iv) face = p, vertices = 6, edge = 12

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ P + 6 = 12 + 2

⟹ P + 6 = 14

⟹ P = 14-6

⟹ P = 12.

Given that (v) face = 6, vertices = q, edge = 12

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ 6 + q = 12 + 2

⟹ 6 + q = 14

⟹ q = 14-6

⟹ q = 8

Given that (vi) face = 8, vertices = 11,edge = r

By using Euler’s formula

We know that

Face + vertices = edge + 2

⟹ 8 + 11 = r + 2

⟹ 19 = r + 2

⟹ r = 19-2

⟹r = 17