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If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:
- a)81∘
- b)54∘
- c)108∘
- d)72∘
Correct answer is option 'D'. Can you explain this answer?
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If an angle of a parallelogram is two-third of its adjacent angle, the...
To find the smallest angle of a parallelogram when one angle is two-thirds of its adjacent angle, we can start by understanding the properties of a parallelogram.
Properties of a Parallelogram:
1. Opposite sides are parallel.
2. Opposite angles are equal.
3. Adjacent angles are supplementary (their sum is 180 degrees).
Let's assume one angle of the parallelogram is x degrees. According to the given condition, another angle will be two-thirds of x, which means it will be (2/3)x degrees.
Using the property of a parallelogram that opposite angles are equal, we can conclude that the opposite angle to x will also be x degrees, and the opposite angle to (2/3)x will also be (2/3)x degrees.
Now, let's find the sum of adjacent angles. Since adjacent angles in a parallelogram are supplementary, we have:
x + (2/3)x = 180 degrees
Combining like terms, we get:
(5/3)x = 180 degrees
To isolate x, we multiply both sides of the equation by (3/5):
x = (180 degrees) * (3/5)
x = 108 degrees
Therefore, the smallest angle of the parallelogram is x, which is equal to 108 degrees.
Hence, the correct answer is option 'c) 108'.
Properties of a Parallelogram:
1. Opposite sides are parallel.
2. Opposite angles are equal.
3. Adjacent angles are supplementary (their sum is 180 degrees).
Let's assume one angle of the parallelogram is x degrees. According to the given condition, another angle will be two-thirds of x, which means it will be (2/3)x degrees.
Using the property of a parallelogram that opposite angles are equal, we can conclude that the opposite angle to x will also be x degrees, and the opposite angle to (2/3)x will also be (2/3)x degrees.
Now, let's find the sum of adjacent angles. Since adjacent angles in a parallelogram are supplementary, we have:
x + (2/3)x = 180 degrees
Combining like terms, we get:
(5/3)x = 180 degrees
To isolate x, we multiply both sides of the equation by (3/5):
x = (180 degrees) * (3/5)
x = 108 degrees
Therefore, the smallest angle of the parallelogram is x, which is equal to 108 degrees.
Hence, the correct answer is option 'c) 108'.
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