We know that all the sides are equal in a rhombus

Consider △ ABD

We get

AB = AD and

∠ ABD = ∠ ADB

It can be written as

x = y ……. (1)

Consider △ ABC

We get

AB = BC and

∠ CAB = ∠ ACB

We know that

∠ ACB = 40o

By using the sum property of a triangle

∠ B + ∠ CAB + ∠ ACB = 180o

By substituting values in the above equation

∠ B + 40o + 40o = 180o

On further calculation

∠ B = 180o – 40o – 40o

By subtraction

∠ B = 180o – 80o

So we get

∠ B = 100o

∠ DBC can be written as

∠ DBC = ∠ B – xo

By substituting the values

∠ DBC = 100o – xo

From the figure we know that ∠ DBC and ∠ ADB are alternate angles

∠ DBC = ∠ ADB = yo

By substituting the value of ∠ DBC

100o – xo = yo

Consider the equation (1) we know that x = y

100o – xo = xo

On further calculation

2xo = 100o

By division

xo = 50o

Therefore, x = y = 50o.

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