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In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?
Most Upvoted Answer
In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D =...
Solution:
A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. The sum of opposite angles in a cyclic quadrilateral is 180 degrees.
Let's find the value of x and y using the given angles:
- Angle A + Angle B + Angle C + Angle D = 360 degrees (sum of angles in a quadrilateral)
- (2x+4) + (y-3) + (2y+10) + (4x-5) = 360
- 6x + 3y + 6 = 360
- 6x + 3y = 354
- 2x + y = 118
We have one equation with two variables, so we can't solve for x and y exactly. However, we can find the values of x and y that satisfy the equation by guessing and checking or using substitution. One possible solution is x = 17 and y = 84.
Now that we know the values of x and y, we can find the four angles:
- Angle A = 2x+4 = 38 degrees
- Angle B = y-3 = 81 degrees
- Angle C = 2y+10 = 178 degrees
- Angle D = 4x-5 = 67 degrees
Therefore, the four angles are 38 degrees, 81 degrees, 178 degrees, and 67 degrees.
A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. The sum of opposite angles in a cyclic quadrilateral is 180 degrees.
Let's find the value of x and y using the given angles:
- Angle A + Angle B + Angle C + Angle D = 360 degrees (sum of angles in a quadrilateral)
- (2x+4) + (y-3) + (2y+10) + (4x-5) = 360
- 6x + 3y + 6 = 360
- 6x + 3y = 354
- 2x + y = 118
We have one equation with two variables, so we can't solve for x and y exactly. However, we can find the values of x and y that satisfy the equation by guessing and checking or using substitution. One possible solution is x = 17 and y = 84.
Now that we know the values of x and y, we can find the four angles:
- Angle A = 2x+4 = 38 degrees
- Angle B = y-3 = 81 degrees
- Angle C = 2y+10 = 178 degrees
- Angle D = 4x-5 = 67 degrees
Therefore, the four angles are 38 degrees, 81 degrees, 178 degrees, and 67 degrees.
Community Answer
In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D =...
A+C=180
B+D=180
(opposite angles of a cyclic quadrilateral)
A+C=180
2x+4+2y+10=180
2x+2y=180-14=166
x+y=83. -(1)
B+D=180
4x-5+y+3=180
4x+y-2=180
4x+y=182. -(2)
On subtracting eq-1 from eq-2
We get
3x=99
x=99/3=33
y+33=83
y=83-33=50
A=2x+4=2*33+4=66+4=70
B=y+3=50+3=53
C=2y+10=2*50+10=100+10=110
D=4x-5=4*33-5=132-5=117
B+D=180
(opposite angles of a cyclic quadrilateral)
A+C=180
2x+4+2y+10=180
2x+2y=180-14=166
x+y=83. -(1)
B+D=180
4x-5+y+3=180
4x+y-2=180
4x+y=182. -(2)
On subtracting eq-1 from eq-2
We get
3x=99
x=99/3=33
y+33=83
y=83-33=50
A=2x+4=2*33+4=66+4=70
B=y+3=50+3=53
C=2y+10=2*50+10=100+10=110
D=4x-5=4*33-5=132-5=117
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In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?
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In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?.
In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?.
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