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The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian?
Verified Answer
The angles of a quardilateral are in A.P. and greatest is double the l...
We know that the sum of all interior angles of a quadrilateral is 360
let x, x + d, x + 2d, x + 3d be the angles
x + (x + d) + (x + 2d) + (x + 3d) = 360
4x + 6d = 360
also the greatesr angle x + 3d = 2x
x = 3d
Substitute this value of x in equation 1
4(3d) + 6d = 360
12d + 6d = 360
18d = 360
d = 20 degrees
x = 60 degree or pi/3 radians (least angle)
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Most Upvoted Answer
The angles of a quardilateral are in A.P. and greatest is double the l...
Given Information:
- Angles of a quadrilateral are in A.P.
- The greatest angle is double the least angle.
Explanation:
- Let the four angles be A, B, C, and D.
- Since the angles are in A.P., we can represent them as A, A + d, A + 2d, and A + 3d.
- Given that the greatest angle is double the least angle, we have A + 3d = 2A.
- Solving the equation, we get A = 3d.
Calculating the least angle:
- Substitute A = 3d in the A.P. sequence: A, A + d, A + 2d, and A + 3d.
- The angles become 3d, 4d, 5d, and 6d.
- The least angle is 3d.
Converting to radians:
- To find the least angle in radians, we know that 180 degrees = π radians.
- So, the least angle in radians = 3d * π / 180.
Final Answer:
- The least angle in radians is 3d * π / 180.
- Angles of a quadrilateral are in A.P.
- The greatest angle is double the least angle.
Explanation:
- Let the four angles be A, B, C, and D.
- Since the angles are in A.P., we can represent them as A, A + d, A + 2d, and A + 3d.
- Given that the greatest angle is double the least angle, we have A + 3d = 2A.
- Solving the equation, we get A = 3d.
Calculating the least angle:
- Substitute A = 3d in the A.P. sequence: A, A + d, A + 2d, and A + 3d.
- The angles become 3d, 4d, 5d, and 6d.
- The least angle is 3d.
Converting to radians:
- To find the least angle in radians, we know that 180 degrees = π radians.
- So, the least angle in radians = 3d * π / 180.
Final Answer:
- The least angle in radians is 3d * π / 180.
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The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian?
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The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian?.
The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of a quardilateral are in A.P. and greatest is double the least. find least angle in radian?.
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