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In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .?
Most Upvoted Answer
In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1...
Let angles A,B,C,D be 1x,2x,4x,5x respectively.
We know that Sum of angles of a quadrilateral=180 degree,
Then,
Angle(A+B+C+D)= 180 degree
1x+2x+4x+5x = 180
12x=180
x=180/12
x=15
Now, Putting the value of x in the ratios, we get:
Angle A=1x= 15
Angle B=2x=30
Angle C=4x=60
Angle D=5x=75
Hence the measure of all the angles of the quadrilateral are 15, 30, 60 and 75 respectively.
HOPE IT HELPS :)
We know that Sum of angles of a quadrilateral=180 degree,
Then,
Angle(A+B+C+D)= 180 degree
1x+2x+4x+5x = 180
12x=180
x=180/12
x=15
Now, Putting the value of x in the ratios, we get:
Angle A=1x= 15
Angle B=2x=30
Angle C=4x=60
Angle D=5x=75
Hence the measure of all the angles of the quadrilateral are 15, 30, 60 and 75 respectively.
HOPE IT HELPS :)
Community Answer
In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1...
To find the angles of quadrilateral ABCD given their ratio, follow these steps:
Understanding the Problem
- The angles A, B, C, and D are in the ratio of 1:2:4:5.
- This means we can express each angle in terms of a variable (let's call it x):
- Angle A = 1x
- Angle B = 2x
- Angle C = 4x
- Angle D = 5x
Sum of Angles in a Quadrilateral
- The sum of the interior angles in any quadrilateral is always 360 degrees.
Setting Up the Equation
- According to the relationship we established:
- 1x + 2x + 4x + 5x = 360
- Simplifying the left side gives:
- 12x = 360
Solving for x
- To find x, divide both sides by 12:
- x = 360 / 12
- x = 30
Calculating Each Angle
- Now substitute x back into the expressions for each angle:
- Angle A = 1x = 1(30) = 30 degrees
- Angle B = 2x = 2(30) = 60 degrees
- Angle C = 4x = 4(30) = 120 degrees
- Angle D = 5x = 5(30) = 150 degrees
Final Angles of Quadrilateral ABCD
- The measures of the angles are:
- Angle A = 30 degrees
- Angle B = 60 degrees
- Angle C = 120 degrees
- Angle D = 150 degrees
This methodical approach allows us to determine the angles of the quadrilateral efficiently.
Understanding the Problem
- The angles A, B, C, and D are in the ratio of 1:2:4:5.
- This means we can express each angle in terms of a variable (let's call it x):
- Angle A = 1x
- Angle B = 2x
- Angle C = 4x
- Angle D = 5x
Sum of Angles in a Quadrilateral
- The sum of the interior angles in any quadrilateral is always 360 degrees.
Setting Up the Equation
- According to the relationship we established:
- 1x + 2x + 4x + 5x = 360
- Simplifying the left side gives:
- 12x = 360
Solving for x
- To find x, divide both sides by 12:
- x = 360 / 12
- x = 30
Calculating Each Angle
- Now substitute x back into the expressions for each angle:
- Angle A = 1x = 1(30) = 30 degrees
- Angle B = 2x = 2(30) = 60 degrees
- Angle C = 4x = 4(30) = 120 degrees
- Angle D = 5x = 5(30) = 150 degrees
Final Angles of Quadrilateral ABCD
- The measures of the angles are:
- Angle A = 30 degrees
- Angle B = 60 degrees
- Angle C = 120 degrees
- Angle D = 150 degrees
This methodical approach allows us to determine the angles of the quadrilateral efficiently.
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In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .?
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In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .? 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 In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .?.
In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .? 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 In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a quadrilateral ABCD , the angles A,B,C and D are in the ratio of 1:2:4:5 find the measure of each angles of the quadrilateral? Can you answer and explain detaily this .?.
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