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Q.

If an angle of a parallelogram is two-third of its adjacent angle, find all the four angles.


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a

45,45,135,135

b

55,45,135,135

c

45,55,135,135

d

45,65,135,135 

answer is A.

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Detailed Solution

Concept- Present a parallelogram, we must determine all four angles. Each angle is given as a fraction of the angle next to it. For this, we will first assume that the neighboring angle is a variable of any kind, and then we will take the angle that is specified as a percentage of the adjacent angles. Applying the parallelogram theory results in a total of neighboring angles of Question Image. We can obtain the two angles by subtracting the total of the angles from Question Image to get the variable, and we can find all four angles by applying the idea that a parallelogram has equal opposing angles.
Step 1: A parallelogram with an angle that is two thirds of its neighboring angles is handed to us.
Question ImageLet's take a parallelogram A B C D in which let us assume Question Image and Question Image. Since sum of adjacent angles is Question Image. On forming the equation we get
Question ImageQuestion ImageOn adding the terms by taking L.C.M
Question ImageQuestion ImageOn dividing by 4
Question ImageOn solving the equation we get
Question ImagePutting the value of Question Image for Question Image we get
Question ImageQuestion ImageStep2: As we know that in parallelograms opposite angles are equal then Question Image and Question Image as they form a pair of opposite angles. Hence, Question Image and Question ImageSo, the four angles are 45,45,135,135
Hence, the correct option is 1.
 
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