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Question

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


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Solution

Step 1: Use relationship between adjacent angles to form an equation

Let the two adjacent angles be x,y

According to given condition,

x=23y ...(i)

The sum of adjacent angles is 180

Therefore, x+y=180 ...(ii)

Step 2 : Find the value of x and y

From (i),(ii)

23y+y=180

53y=180

y=108

x=72

Step 3: Find the remaining angles of the parallelogram

The opposite angles of a parallelogram are equal.

So, angle opposite to x will also be 72,

And, similarly, angle opposite y will be 108.

Hence all the angles of the parallelogram are 108,72,108,72


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