Question

7. The difference of the measures two adjacen
angles of a parallelogram is 50. Find the
measure of all its angles.​

Answer 1

Answer:

Let us assume that all the angles of the parallelogram are a° , b° , x° , y°

We know that sum of adjacent angles in a quadrilateral is 180°

Let us assume that the angles are x° , y°

So, x° + y° = 180° and x° - y° = 30°

Solving both the equations we get x = 105° and y = 75°

Now we already know that sum of adjacent angles in a quadrilateral is 180°.

So, x + a = 180°

a = 75°  (substituting x = 105°)

y° + b° = 180°

b = 105° (substituting y = 75°)

Hence the angles of the quadrilateral are 75° , 75° , 105° , 105°.

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