Question

If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.

Answer 1

Given,

The measures of 2 adjacent angles of a parallelogram as 1:2.

To Find,

The measures of all the angles of a parallelogram.

Solution,

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Refer to picture for diagrammatical representation.

As per the properties of a parallelogram, we know that the sum of the adjacent angles of a parallelogram is $180^o$.

So, taking the given measures as 1x and 2x, we can write down as →

$1x+2x=180^o$

$3x=180^o$

Therefore,

$x=180/3=60$

So the measures of 1x and 2x are 60 and 120.

As per the properties of a parallelogram, the opposite angles of a parallelogram have the same measure. So, the angle opposite $60^o$ has the measure $60^o$ and the angle opposite $120^o$ has the measure $120^o$.

So the measures of the angles of the parallelogram are:

$60^o,120^o,60^oand120^o$

Proof,

We know that the sum of all the angles of any quadrilateral is 360 degrees.

$60^o+120^o+60^o+120^o=360^o$

$360^o=360^o$

Hence proved.

Properties used,

• Sum of the adjacent angles of a parallelogram is 180 degrees.
• Opposite angles of a parallelogram have the same measure.