Answer :

Given, AB = AD

BC = CD


AC which is common to both ∆ADC and ∆ABC.


So, DAC = CAB = 30 as AB = AD and AC which is common.


And, DCA = ACB = 50 as BC = CD and AC which is common.


Now, we know sum of all interior angles of a triangle is 180⁰.


In ∆ADC,


a + d + c = 180⁰


30⁰ + d + 50⁰ = 180


80⁰ + d = 180⁰


d = 180⁰-80⁰


d = 100⁰


In ∆ABC,


a + b + c = 180⁰


30⁰ + b + 50⁰ = 180⁰


80⁰ + b = 180⁰


b = 180⁰-80⁰


b = 100⁰


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