Using the information, given in each of the following figures, find the values of a and b.

In △ ADE,

⇒ AD = AE (Given)

∴ ∠ADE = ∠AED (Angles opposite to equal sides are equal)

⇒ 180° - ∠ADE = 180° - ∠AED

⇒ ∠ADC = ∠AEB

In △ ABE and △ CAD,

⇒ ∠EAB = ∠CAB (Given)

⇒ ∠ADC = ∠AEB (Proved above)

⇒ AE = AD (Given)

∴ △ ABE ≅ △ CAD (By A.S.A. axiom)

We know that,

Corresponding sides of congruent triangle are equal.

∴ AC = AB and CD = EB.

Considering CD = EB,

⇒ a = 3b ………(1)

Considering AC = AB,

⇒ 2a + 2 = 7b - 1

Substituting value of a from equation (1) in above equation, we get :

⇒ 2(3b) + 2 = 7b - 1

⇒ 6b + 2 = 7b - 1

⇒ 7b - 6b = 2 + 1

⇒ b = 3.

Substituting value of b in equation (1), we get :

⇒ a = 3(3) = 9.

Hence, a = 9 and b = 3.