Question

9. Two adjacent angles of a parallelogram are in the ratio 2:3. Find the measure of
the angles.
10 Trd​

Answer 1

Answer:

72°,72°,108°,108°

Step-by-step explanation:

Let ABCD is the given parallelogram and angle A and angle B be 2x and 3x.

As we know that the opposite angle of a parallelogram is equal and sum of all four angles is 360.

Now, 2x+2x+3x+3x=360°

10x=360°

x=360°÷10

x=36°

So,angle A=2×36=72°

angle B=3×36=108°

angle C=angle A=72°

angle D=angle B=108°

Answer 2

Required Answer :

The two adjacent angles of a parallelogram are 72° and 108°.

Given :

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

To find :

• Measure of the angles

Solution :

The sum of the adjacent angles of a parallelogram is equal to 180°.

To find the measure of the two adjacent angles, we will assume the two angles of parallelogram according to the ratio given in the question. Then add both the angles and keep them equal to 180°

Let,

• First angle of parallelogram = 2x
• Second angle of parallelogram = 3x

→ First angle + Second angle = 180°

→ 2x + 3x = 180°

→ 5x = 180°

→ x = 180°/5

→ x = 36°

→ The value of x = 36°

Substituting the value of 'x' in the adjacent angles :-

→ First angle = 2x

→ First angle = 2(36°)

→ First angle = 72°

→ Second angle = 3x

→ Second angle = 3(36°)

→ Second angle = 108°

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Verification :

We can verify the measure of the two adjacent angles by adding them. If the sum of the two angles will be equal to 180° (sum of adjacent angles of parallelogram is always equal to 180°) then the value is right.

→ First angle + Second angle

→ 72° + 108°

→ 180°

Sum of adjacent angles of parallelogram = 180°

Hence, verified!