Question

ABCD s a cyclic quadrilateral, if ∠A = 4x, ∠B= 3y, ∠C= 5x, and ∠D= 7y, then x and y are equal to--​

Answer 1

Answer:

sum of opp. angles = 180°

a + c = 180

4x+5x = 180

9x = 180

X = 20°

b + d = 180°

3y + 7y = 180

10y = 180

y = 18

Answer 2

Answer:

x = 20 and

y = 18

Step-by-step explanation:

Explanation:

Given, ABCD is a cyclic quadrilateral

∠A = 4x ,∠B = 3y ,∠C = 5x and ∠D = 7y .

So , we know that ,a cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle .

Therefore we draw a circle and a quadrilateral which inscribe in the circle and plot the angle which is given in the question.

Step1:

Here we have .

∠B +∠D = 180 °

(sum of either pair of opposite angle of a cyclic  quadrilateral is 180°)

⇒ 3y+7y = 180

⇒10y = 180  

⇒ y = 18

Step 2:

Again,

∠A +∠C = 180 °

⇒ 4x+ 5x = 180

⇒9x = 180 ⇒ x = 20

Final answer :

Hence , the value of x and y is 20 and 18.