Question

the opposite angle of a parallelogram are (3x-2) and (50-x) find the measure of each angle of a parallelogram?​

Answer 1

Given:-

• Opposite angle of a parallelogram are (3x - 2)° and (50 - x)°

To Find:-

• All the angles of the parallelogram.

Note:-

• Refer to the attachment for the diagram.

Solution:-

Here as the opposite angles of the parallelogram is given, we can apply the theorem that says:-

• The opposite angles of a parallelogram is always equal.

Hence,

We can say that, In this parallelogram

∠BAD = ∠BCD

= (3x - 2)° = (50 - x)

= 3x - 2 = 50 - x

= 3x + x = 50 + 2

= 4x = 52

=> x = 52/4

=> x = 13°

Putting the value of x in the given angles

∠BAD = 3x - 2 = 3 × 13 - 2 = 39 - 2 = 37°

∠BCD will be equal as ∠BAD because they are opposite angles

Hence ∠BCD = 50 - x = 50 - 13 = 37°

Now,

We know that,

• Sum of adjacent sides of a parallelogram is always supplementary.

Let the ∠ABC adjacent to angle ∠BAD be x

Hence,

∠BAD + ∠ABC = 180°

= 37° + x = 180°

=> x = 180° - 37°

=> x = 143°

Now,

∠ABC = ∠CDA = 143° (Opposite angles)

Therefore,

Measure of all the angles of the parallelogram are as follows.

• ∠ABC = 143°
• ∠BCD = 37°
• ∠CDA = 143°
• ∠DAB = 37°

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