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ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5?
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ABCD is a cyclic quadrilateral. Find the value of x and y and thus fin...
To find the value of x and y and the measure of the angles of the cyclic quadrilateral ABCD, we can use the properties of cyclic quadrilaterals.
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. One property of a cyclic quadrilateral is that the opposite angles are supplementary, which means their measures add up to 180 degrees.
Let's solve for x and y using the given information:
1. Opposite angles A and C are supplementary:
2x + 4 = 180 - (4y - 4)
2. Opposite angles B and D are supplementary:
x + 10 = 180 - (5y + 5)
Simplifying the equations:
1. 2x + 4 = 180 - 4y + 4
2x = 180 - 4y
x = (180 - 4y)/2
x = 90 - 2y
2. x + 10 = 180 - 5y - 5
x = 180 - 5y - 5 - 10
x = 165 - 5y
Setting the two expressions for x equal to each other:
90 - 2y = 165 - 5y
Solving for y:
3y = 75
y = 25
Now that we have found the value of y, we can substitute it back into one of the equations to find x:
x = 165 - 5(25)
x = 165 - 125
x = 40
Therefore, x = 40 and y = 25.
To find the measure of the angles of the quadrilateral:
Angle A = 2x = 2(40) = 80 degrees
Angle B = x + 10 = 40 + 10 = 50 degrees
Angle C = 4y - 4 = 4(25) - 4 = 96 degrees
Angle D = 5y + 5 = 5(25) + 5 = 130 degrees
So the measure of the angles of the quadrilateral ABCD are:
Angle A = 80 degrees
Angle B = 50 degrees
Angle C = 96 degrees
Angle D = 130 degrees
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. One property of a cyclic quadrilateral is that the opposite angles are supplementary, which means their measures add up to 180 degrees.
Let's solve for x and y using the given information:
1. Opposite angles A and C are supplementary:
2x + 4 = 180 - (4y - 4)
2. Opposite angles B and D are supplementary:
x + 10 = 180 - (5y + 5)
Simplifying the equations:
1. 2x + 4 = 180 - 4y + 4
2x = 180 - 4y
x = (180 - 4y)/2
x = 90 - 2y
2. x + 10 = 180 - 5y - 5
x = 180 - 5y - 5 - 10
x = 165 - 5y
Setting the two expressions for x equal to each other:
90 - 2y = 165 - 5y
Solving for y:
3y = 75
y = 25
Now that we have found the value of y, we can substitute it back into one of the equations to find x:
x = 165 - 5(25)
x = 165 - 125
x = 40
Therefore, x = 40 and y = 25.
To find the measure of the angles of the quadrilateral:
Angle A = 2x = 2(40) = 80 degrees
Angle B = x + 10 = 40 + 10 = 50 degrees
Angle C = 4y - 4 = 4(25) - 4 = 96 degrees
Angle D = 5y + 5 = 5(25) + 5 = 130 degrees
So the measure of the angles of the quadrilateral ABCD are:
Angle A = 80 degrees
Angle B = 50 degrees
Angle C = 96 degrees
Angle D = 130 degrees
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ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5?
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ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5? 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 ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5?.
ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5? 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 ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a cyclic quadrilateral. Find the value of x and y and thus find the measure of the angles of the quadrilateral if angle A is 2x 4 angle B is x 10 angle C is 4y-4 and angle D is 5y 5?.
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