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Q.

Given a rhombus ABCD, the measure of angles x and y for the figure below are.


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a

x = 31 o   and y = 59 o  

b

x = 21 o   and y = 59 o  

c

x = 31 o   and y = 39 o  

d

x = 31 o   and y = 79 o   

answer is A.

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Detailed Solution

Given a rhombus ABCD.
As, AO is an angle bisector of angle x.Question Image x=   1 2 ×BAD x= 1 2 ×   62 0 x= 31 0  
Now in triangle CDO, the sum of interior angle of a triangle is 180 o  .
CDO+DOC+ OCD= 18 0 o CDO+9 0 o  +  31 o =18 0 o CDO= 59 o   As, ABCD is a rhombus it’s all sides are equal, therefore BC = CD.
CDO=y y= 59 o   The measure of x and y are 31 0   and 59 o   respectively.
Hence, option 1 is correct.
 
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