Question

The Angles of cyclic Quadrilateral ABCD are A = ( 6x +10) , B= (5x), C= ( x+Y) and D= (3y -10) Find the value of X and Y. ​

Answer 1

$\bold \red{Answer}$

As ABCD is a cyclic quadrilateral, we have

∠A+∠C=180° -----(The sum of the opposite angles of a cyclic quadrilateral =180°)

⟹ 6x+10°+x+y=180°

⟹ 7x+y=170°----(1) and ∠B+∠D=180°----(The sum of the opposite angles of a cyclic quadrilateral =180°)

⟹ (3y−10)+5x=180°

⟹ 3y+5x=190°------(2)

Solving (1) and (2), we have,

x=20°

y=30°

A=6x+10=6×20°+10°=130°

B=5x=5×20°=100°

C=x+y=30°+20°=50°

D=3y−10=3×30−10=80

Answer 2

Question:

The Angles of cyclic Quadrilateral ABCD are A = ( 6x +10) , B= (5x), C= ( x+Y) and D= (3y -10) Find the value of X and Y.

Answer:

x = 20° and y = 30°

Step-by-step explanation:

The cyclic quadrilateral, the sum of opposite angle is 180°.

So, / A + / C = 180°

= (6x + 10)° + ( x + y)° = 180°

= (7x + y + 10)° = 180° (Equation 1)

/ B + / D = 180°

= 5x° + ( 3y - 10)° = 180°

= (5x + 3y - 10)° = 180° ( Equation 2)

• Solving Equations 1 and 2 , we get x = 20° and y = 30°