Question

In the given figure,find the value of x and y where o is the center of the circle.​

Answer 1

Answer:

ABCD is a quadrilateral;

---> ∠A+∠B+∠C+∠D=360°

Sum of the opposite sides of a quadrilateral is 180°

∴ ∠A+∠C=180°

---> 2y+4° +4x-4°=180° ----------[1]

And ∠B+∠D=180°

---> y+10° +5x+5°=180°---------[2]

On adding equation 1 and 2,we get;

2y+4°+5x+5°+4x-4°+y+10°=360°--------------[3]

Equation 1;

-----> 2y+4°+4x-4°=180°

----->2y+4x=180°

----->y+2x=90°

----->y=90°-2x     ------------[4]

Put equation 4 in equation 3;

-----> 2y+4°+5x+5°+4y-4°+y+10°=360°

-----> 2y+4y+y+5x+15°=360°

-----> 7y+5x+15°=360°

-----> 7(90°-2x)=360°-15°

-----> 630°-14x=345°

-----> -14x=345°-630°

-----> -14x= -185°

-----> 14x=185°

-----> x=185/14=46.25°

∴ Substitute the value of x in equation 4;

   y= 90°-2x

--> y=90°-2*46.25°

--> y=90°-92.5°

--> y= -2.5°

∴ x=46.25° ,y= -2.5°

Step-by-step explanation: