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°
☛ Related Questions:
Math worksheets and
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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°
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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.
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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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