Question

ABCD Is a cyclic quadrilateral if angle A = 4x ,angle B = 3y angle C = 2x and angle D= 15y then x and y are equal to

Answer 1

Answer:

Answer:

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We know that the sum of the opposite angles of a cyclic quadrilateral is 180o. In the cyclic quadrilateral ABCD, angles A and C and the angle B and D form pairs of opposite angles.

∴∠A+∠C=180o and ∠B+∠D=180o

⇒2x−1+2y+15=180 

      and y+5+4x−7=180

⇒2x+2y=166 

      and 4x+y=182

⇒x+y=83 ..(i)

and, 4x+y=182 ..(ii)

Subtracting equation (i) from equation (ii), we get

3x=99⇒x=33

Substituting x=33 in equation (i), we get y=50

Hence, ∠A=(2×33−1)o=65o,∠B=(y+5)

Answer 2

Answer:

The correct answer of this question is y is 10 and x = 30.

Step-by-step explanation:

Given - ABCD Is a cyclic quadrilateral .

To Find  - Find the angle A = 4x ,angle B = 3y angle C = 2x and angle D= 15y which is equal to  x and y .

A quadrilateral with all four vertices on a circle is called a cyclic quadrilateral.

∠A = 4x ,∠B = 3y ,∠C = 2x and ∠D = 15y .

Now, according to the question ,

A cyclic quadrilateral's sum of either pair of opposite angles is 180°.

∠B +∠D = 180 °

3y + 15y = 180°

⇒18y = 180°

⇒ y = 10

Again ,

∠A +∠C = 180 °

⇒ 4x+ 2x = 180°

⇒6x = 180 ⇒ x = 30

Hence , the value of x and y is 10 and 30.

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