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