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Question

ABCD is a rhombus such that one of its diagonals is equal to its sides. Then the angles of rhombus ABCD are-

A
45,135,45,135
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B
100,80,100,80
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C
120,60,120,60
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D
60,60,60,60
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Solution

The correct option is B 120,60,120,60

When one side is equal to the diagonal AC , then all sides are equal to AC because all sides of rhombus are equal.
So, in ABC, all sides are equal.
Let measure of angles in ABC be x.
x+x+x=180o [Since, sum of angles is 180o in triangle ]
3x=180o
x=60o
B=60o
In ACD,
Let measure of angles in ACD be x.
x+x+x=180o
3x=180o
x=60o
D=60o
A=60o+60o=120o
C=60o+60o=120o
The angles of rhombus ABCD are 120o,60o,120o,60o.

1245584_84621_ans_c932c5771a1341f7906dac062b662182.png

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