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Q.

Find the values of x and y in the following kite and choose the option which represents the same.


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a

x= 80 ° and y= 110 °

b

x= 110 ° and y= 80 °

c

x= 60 ° and y= 100 °

d

x= 100 ° and y= 80 °  

answer is A.

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Detailed Solution

Here, we are given a kite and we have to determine the angle measures x and y as indicated in the diagram above.
So, we know that in the case of a kite, the angles formed at the point where the two unequal sides meet are always equal.
Now, in the given diagram, it can be observed that the angle formed at the meeting point of the unequal sides, measures 110 ° .
So, as per the property of a kite, the angle opposite to the angle measure of 110 ° , will also be the same. Therefore, ∠x= 110 ∘ .
Now, according to the angle sum property of any quadrilateral, the sum of all the interior angles of a quadrilateral equals 360 ° .
Using this property, we will find the value of y, as follows,
110 ∘ +x+y+ 60 ∘ = 360 ∘ 110 ∘ + 60 ∘ + 110 ∘ +x= 360 ∘ 280 ° +x= 360 ° x= 360 ° − 280 ° x= 80 °
So, the value of x= 80 ° and y= 110 ° .
Hence, the correct option is (1).
 
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