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In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral?
Most Upvoted Answer
In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : ...
Let the a,b,c,d angles be x, 2x, 4x and 5x respectively
a+b+c+d=360
x+2x+4x+5x=360
12x=360
x=360/12=30
a=x=30
b=2x=2*30=60
c=4x=4*30=120
d=5x=5*30=150
a+b+c+d=360
x+2x+4x+5x=360
12x=360
x=360/12=30
a=x=30
b=2x=2*30=60
c=4x=4*30=120
d=5x=5*30=150
Community Answer
In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : ...
Understanding the Angle Relationships
In quadrilateral ABCD, the angles a, b, c, and d are given in the ratio 1:2:4:5. This means we can express each angle as a multiple of a common variable, say x.
Assigning Variables to Angles
- Angle a = 1x
- Angle b = 2x
- Angle c = 4x
- Angle d = 5x
Sum of Angles in a Quadrilateral
The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the equation:
1x + 2x + 4x + 5x = 360
Simplifying the Equation
Combining the terms, we have:
12x = 360
Solving for x
To find the value of x, divide both sides by 12:
x = 30
Calculating Each Angle
Now, substituting 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 Measures of Each Angle
Thus, the measures of the angles in quadrilateral ABCD are:
- Angle a = 30 degrees
- Angle b = 60 degrees
- Angle c = 120 degrees
- Angle d = 150 degrees
These angles satisfy the ratio 1:2:4:5 and add up to 360 degrees, confirming our calculations are correct.
In quadrilateral ABCD, the angles a, b, c, and d are given in the ratio 1:2:4:5. This means we can express each angle as a multiple of a common variable, say x.
Assigning Variables to Angles
- Angle a = 1x
- Angle b = 2x
- Angle c = 4x
- Angle d = 5x
Sum of Angles in a Quadrilateral
The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the equation:
1x + 2x + 4x + 5x = 360
Simplifying the Equation
Combining the terms, we have:
12x = 360
Solving for x
To find the value of x, divide both sides by 12:
x = 30
Calculating Each Angle
Now, substituting 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 Measures of Each Angle
Thus, the measures of the angles in quadrilateral ABCD are:
- Angle a = 30 degrees
- Angle b = 60 degrees
- Angle c = 120 degrees
- Angle d = 150 degrees
These angles satisfy the ratio 1:2:4:5 and add up to 360 degrees, confirming our calculations are correct.
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In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral?
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In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral? covers all topics & solutions for Class 8 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 1 : 2: 4:5. Find the measure of each angle of the quadrilateral?.
In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a quadrilateral ABCD the angles a, b, c and d are in the ratio 1 : 2: 4:5. Find the measure of each angle of the quadrilateral? covers all topics & solutions for Class 8 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 1 : 2: 4:5. Find the measure of each angle of the quadrilateral?.
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