Question

the measure of two adjacent angle of a parallelogram are in the ratio 3:2. find the measure of each of the angle of the parallelograms​

Answer 1

Answer :

The measure of each adjacent angle :-

• First adjacent angle = 108°
• Second adjacent angle = 72°

Given :

• Ratio of two adjacent angles of a parallelogram = 3 : 2

To find :

• Measure of each angle

Concept :

As mentioned in the question, the ratio is of two adjacent angles of a parallelogram. And the sum of adjacent angles is equal to 180°. So, firstly assume the two angles as 3a and 2a. To find the value of 'a' add both the angles and keep them equal to 180°. After getting the value of a, substitute it in both the adjacent angles, the resultant value will be our required answer.

Solution :

Let,

• First adjacent angle of parallelogram = 3a
• Second adjacent angle of parallelogram = 2a

★ Sum of angles of adjacent angles of a parallelogram = 180°

➪ 3a + 2a = 180°

➪ 5a = 180°

➪ Transposing 5 to the right hand side.

➪ a = 180° ÷ 5

➪ a = 36°

The value of a = 36°

Substituting the value of a in the adjacent angles of parallelogram :-

→ First adjacent angle = 3a = 3 × 36° = 108°

→ Second adjacent angle = 2a = 2 × 36° = 72°

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VERIFICATION :

To verify the value of both the adjacent angles of parallelogram, add both the angles. If they sum upto 180° (∵sum of adjacent angles = 180°) Then their values are right.

Measure of the adjacent angles :-

• The two adjacent angles are 108° and 72°.

Adding both the angles :-

→ 108° + 72°

→ 180°

Sum of adjacent angles = 180°.

HENCE, VERIFIED.