Class 9 Exam > Class 9 Questions > If an angle of a parallelogram is two-third o...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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'.
Free Test
FREE
| Start Free Test |
Community Answer
If an angle of a parallelogram is two-third of its adjacent angle, the...
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer?
Question Description
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer?.
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer?.
Solutions for If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a)81b)54c)108d)72Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup