Class 10 Exam > Class 10 Questions > In a cyclic quadrilateral ABCD.angle A = 2x +...
Start Learning for Free
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
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?
Question Description
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?.
Solutions for In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? defined & explained in the simplest way possible. Besides giving the explanation of
In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles?, a detailed solution for In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? has been provided alongside types of In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? theory, EduRev gives you an
ample number of questions to practice In a cyclic quadrilateral ABCD.angle A = 2x + 4, B =y+3, C= 2y+10, D = 4x-5.Find the four angles? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup