Question

Using the information given of the following figure, find the values of a and b.

Answer 1

In ΔAEB and ΔCAD,
∠EAD = ∠CAD .........[Given]
∠ADC = ∠AEB .......[∵ ∠ADE = ∠AED { AE = AD }180° − ∠ADE = 180° − ∠AED = ∠ADC = ∠AEB] 
AE = AD .........[Given]
∴ ΔAEB ≅ ΔCAD ....[ASA]
AC = AB .......[By C.P.C.T.]
2a + 2 = 7b − 1
⇒ 2a − 7b = − 3 ....(i)
CD = EB
⇒ a = 3b ....(ii)
Solving (i) and (ii), We get,
a = 9, b = 3