Find the value of x if two adjacent angles of a parallelogram are

Solution:

Given that the adjacent angles of a parallelogram are in the ratio 3:2.

Thus, the angles are 3x and 2x respectively.

We know that the sum of the measures of adjacent angles is 180° for a parallelogram.

∠A + ∠B = 180°

3x + 2x = 180°

5x = 180°

x = 180°/5

x = 36°

Thus, one of the angles = 3x

3(36°) = 108°

The other angle is 2x

2(36°) = 72°

The other two angles are 72° and 108° since opposite angles of a parallelogram are equal.

Thus, the measures of the angles of the parallelogram are 108°, 72°, 108°, and 72°

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 5

Summary:

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. The measures of each of the angles of the parallelogram are 108°, 72°, 108°, and 72°

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1. Example 1: Two adjacent angles of a parallelogram are (3x - 4) and (3x + 16). Find the value of x and the measure of each angle.

   Solution: If the adjacent angles of a parallelogram are (3x - 4) and (3x + 16), the value of x can be calculated using the following steps.

   • Step 1: Since the adjacent angles of a parallelogram are supplementary, we can write it as, (3x - 4) + (3x + 16) = 180.
   • Step 2: Solving this, we get, 6x + 12 = 180. So, the value of x = 28.
   • Step 3: Now, after substituting the value of x as 28 in (3x - 4), we get, (3 × 28) - 4 = 84 - 4 = 80°.
   • Step 4: Similarly, the value of the other angle can be calculated by substituting the value of x = 28 in (3x + 16). This means, 3x + 16 = (3 × 28) + 16 = 100°. Therefore, these two adjacent angles are 80° and 100°. It can be verified that they sum up to 180°, that is, 80 + 100 = 180°

2. Example 2: Observe the figure given below and find the value of 'a'.

   

   Solution: It is given that ∠W = (a - 20)° and ∠Z = 115°. We know that the adjacent angles of a parallelogram are supplementary. Therefore, ∠W + ∠Z = 180°. On substituting the given values, we get, a - 20 + 115 = 180. Now, we can find the value of 'a' by solving the equation. That means, a + 95 = 180, so, a = 85.

3. Example 3: If two adjacent angles of a parallelogram are (5x - 5) and (10x + 35). Find the value of x and the ratio of the two angles.

   Solution: If two adjacent angles of a parallelogram are (5x - 5) and (10x + 35), let us first find the value of x using the following steps:

   • Step 1: We know that the adjacent angles of a parallelogram are supplementary, so this can be written as, (5x - 5) and (10x + 35) = 180.
   • Step 2: After solving this, we get, 15x + 30 = 180. This gives the value of x = 10.
   • Step 3: Now, let us substitute the value of x = 10 in (5x - 5), and we get, (5 × 10) - 5 = 50 - 5 = 45°.
   • Step 4: Similarly, the value of the other angle can be calculated by substituting the value of x = 10 in (10x + 35). This means, 10x + 35 = (10 × 10) + 35 = 135°. Therefore, these two adjacent angles are 45° and 135°, and it can be verified that they sum up to 180°, that is, 45 + 135 = 180°.
   • The ratio of the two angles = 45/135 = 1:3

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