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Hey consider the rhombus ABCD,
Given that One of the diagonal say AC is equal to sides.
So AB=BC=CD=AD=AC.
Now, We see that AC divides the rhombus into two triangles namely ∆ABC, ∆ADC
Now consider the angles of rhombus
A = BAC + DAC.
C = DCA + BCA.
B= B
D=D
Now consider each triangle separately,
In ∆ADC.
We know that AD = DC = CA
thus, it is an equilateral triangle as all sides are equal thus all angles are equal
So D= DAC = DCA = 60°
In ∆ABC.
We know that AB = BC = CA
thus, it is an equilateral triangle as all sides are equal thus all angles are equal
So B= BAC = BCA = 60°
Finally we found all angles of rhombus.
1) A = BAC + DAC = 60+60=120°
2) B =60°
3) C = DCA + BCA = 60+60=120°
4) D =60°.
Given that One of the diagonal say AC is equal to sides.
So AB=BC=CD=AD=AC.
Now, We see that AC divides the rhombus into two triangles namely ∆ABC, ∆ADC
Now consider the angles of rhombus
A = BAC + DAC.
C = DCA + BCA.
B= B
D=D
Now consider each triangle separately,
In ∆ADC.
We know that AD = DC = CA
thus, it is an equilateral triangle as all sides are equal thus all angles are equal
So D= DAC = DCA = 60°
In ∆ABC.
We know that AB = BC = CA
thus, it is an equilateral triangle as all sides are equal thus all angles are equal
So B= BAC = BCA = 60°
Finally we found all angles of rhombus.
1) A = BAC + DAC = 60+60=120°
2) B =60°
3) C = DCA + BCA = 60+60=120°
4) D =60°.
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