Q. The angles of a cyclic quadrilatral ABCD are angle A=(6x+10),angle B=(5x),angle C=(x+y),angle D=(3y-10). Find x and y and hence the values of the four angles? If anyone will give the answer with full explanation I will mark it as brainliest.
Answers
answer is:
angle A = 130
angle B = 100
angle C = 50
angle D = 80
Answer:
So we know in a cyclic quadrilateral, the opposite angles sum up to one 180 degrees i.e. angle A + angle C = 180 degrees and angle B + angle D = 180 degrees.
Step-by-step explanation:
Given:
A = 6x + 10
B = 5x
C = x+y
D = 3y - 10
Now,
A + C = 180
Therefore,
6x + 10 + x + y = 180
7x + y = 170 ...(1)
Now,
B + D = 180
5x + 3y - 10 = 180
5x + 3y = 190 ...(2)
L.C.M of the 'y' value in equations (1) and (2) is '3' so multiply the entire equation (1) with '3',
3(7x + y = 170) =
21x + 3y = 510 ...(3)
Subtracting (2) from (3),
21x + 3y = 510
-(5x + 3y = 190) =
21x + 3y = 510
-5x - 3y = -190
= 16x = 320
therefore,
x = 20
substituting the value of 'x' in (1),
7 * 20 + y = 170
140 + y = 170
therefore,
y = 30
Now we substitute the values of both 'x' and 'y' in the expressions they have given for each angle,
A = 6x+ 10
= 6 * 20 + 10
= 120 + 10
= 130 degrees
B = 5x
= 5 * 20
= 100 degrees
C = x + y
= 20 + 30
= 50 degrees
D = 3y - 10
= 3 * 30 - 10
= 90 - 10
= 80 degrees
Now to know if we are correct,
A + C = 130 + 50 = 180 degrees
B + D = 100 + 80 = 180 degrees
Also,
A + B + C + D = 130 + 100 + 50 + 80
= 180 degrees