Question

Q) The measures of all adjacent angles of parallelogram are in the ratio 3:2. find the measure of each of the angles of a parallelogram?​

Answer 1

Given :-

Ratio of the adjacent angles = 3 : 2

Required to find :-

Measure of each of the angle of the parallelogram

Conditions used :-

• Opposite angles are equal

• Sum of two adjacent angles is supplementary

Solution :-

Given information :-

Ratio of the adjacent angles = 3:2

We need to find the measures of all angles in the parallelogram !

So,

Recall the properties of parallelogram

• Opposite angles are equal

So,

The ratio of the adjacent angles is also equal to the ratio of the remaining other two sides because they opposite sides are equal

Similarly ,

• In a parallelogram , all angles will added up to 360°

Because, in any quadrilateral sum of all 4 four angles is equal to 360°

Hence,

we can conclude that

The ratio of given adjacent angles + The ratio of remaining two adjacent sides = 360 °

But,

Let the two adjacent sides be 3x & 2x

So,

3x + 2x + 3x + 2x = 360°

10x = 360°

x = 360°/10

x = 36°

So,

The measures of the adjacent sides are

3 ( 36 ) = 108°

&

2 ( 36 ) = 72°

Similarly ,

The remaining measures of the two angles are ; 108° & 72°

Therefore ,

Measures of the all 4 angles are 108° , 72° , 108° , 72°

Answer 2

Given ,

The ratio of adjacent angles of parallelogram is 3 : 2

Let , the given adjacent angles be 3x and 2x

We know that ,

The opposite angles of parallelogram are equal and the sum of all angles of parallelogram is 360

Thus ,

$\sf \mapsto 3x + 2x + 3x + 2x = 360 \\ \\ \sf\mapsto</p><p>10x = 360 \\ \\ \sf \mapsto</p><p>x = 36$

$\therefore \therefor \sf \underline{The \: angles \: of \: parallelogram \: are \: 108 \: , \: 72 \: , \: 108 \: and \: 72 </p><p>}}$