Question

Find the measure of all four angles of a parellelogram who conscutive angles are in the ratio 1:3

Answer 1

Given :

• The measure of all four angles of a parellelogram who conscutive angles are in the ratio 1:3.

To Find :

• All the four angles of the Parallelogram.

Solution :

We know that,

• Sum of two consecutive interior angles of a parallelogram is equal to 180°

Let,

• First angle of the Parallelogram = x
• Second angle of the Parallelogram = 3x

According to the Question :

• Sum of two interior angles = 180
• x + 3x = 180
• 4x = 180
• x = 180/4
• x = 45°

Therefore :

• First angle of the Parallelogram = x
• First angle of the Parallelogram = 45°

• Second angle of the Parallelogram = 3x
• Second angle of the Parallelogram = 3 × 45
• Second angle of the Parallelogram = 135°

Conclusion :

• As we know that, the opposite angles of a parallelogram are equal.
• Hence, the measure of all the four angles of the Parallelogram are 45° , 135° , 45° and 135°.

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