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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

. We can obtain the two angles by subtracting the total of the angles from

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 Image

Question Image

Let's take a parallelogram A B C D in which let us assume

and

. Since sum of adjacent angles is

. On forming the equation we get

On adding the terms by taking L.C.M

On dividing by 4

On solving the equation we get

Putting the value of

for

we get

Step2: As we know that in parallelograms opposite angles are equal then

and

as they form a pair of opposite angles. Hence,

and

So, the four angles are 45,45,135,135
Hence, the correct option is 1.

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