If ABCD is a rhombus find the values of x and y.
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Step-by-step explanation:
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=40
o
by using the sum property of a triangle
∠B+∠CAB+∠ACB=180
o
By substituting the values in equation
∠B=40
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+40
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=180
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∠B=180
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−80
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∠B=100
o
∠DBC can be written as
∠DBC=∠B−x
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by sbstituting the values
∠DBC=100
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−x
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From the figure we know that ∠DBC and ∠ADB are alternate angles
∠DBC=∠ADB=y
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by subsituting the value of ∠DBC
100
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−y
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=y
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consider the equation (1) we know thatx=y
100
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−x
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=x
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2x
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=100
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x
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=50
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therefore x=y=50
o
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