Question

21. Prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
Using the above, find x and y in Fig. 4.​

Answer 1

HEY MATE HERE IS UR ANSWER.

TAKE A CIRCLE AND DRAW A DIAMETER ON IT .

THEN DRAW A QUADRILATERAL BY EXTENDING ITS SIDES TO BOTH ENDS SO THAT TWO TRIANGLES ARE FORMED.

NOW TAKE A TRIANGLE AND NOTICE THAT THE ANGLE SUBSTENDED BY THE DIAMETER ON THE CIRCLE IS A RIGHT ANGLE .

AND SIMILAR IS ON OTHER SIDE.

SO, BY ADDING BOTH WE GET THAT THE SUM OF THE OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL IS 180° .

NOW , THE QUESTION.

SINCE, ANGLE A + ANGLE C = 180°

SO, X +2 Y + 2X = 180°

=>. 3X+ 2Y = 180°. --------------- (1)

and the other equation is

5Y - X + X + Y = 180°

So, 6Y = 180°

So, Y= 30°

NOW PUTTING IN EQ. 1 , WE GET.

3X + 60 = 180

SO, 3X = 120

SO , X = 40°

HOPE THIS WILL HELP U.

PLZ MARK AS BRAINLEST ......

.AND PLZ FOLLOW ME

Answer 2

Answer:

The value of x=40° and y=30°.

Step-by-step explanation:

As per the data given in the question,

Draw a diameter on a cirlce, and extend 2 triangles on the perimeter on opposite side having base at diameter.

As we know that angle subtended by diameter on perimeter is right angle = $90\°$

So, sum of opposite angles become $90\°+90\°=180\°$

Now, in the question,

∠A+∠C=180° (opposite angles of cyclic quad.)

$x+2y+2x=180\\3x+2y=180.......(i)$

∠B+∠D=180° (opposite angles of cyclic quad.)

$x+y+5y-x=180\\6y=180\\y=30$

putting in (i)

$3x+2\times 30=180\\3x=120\\x=40$

So, x=40° and y=30°.

#SPJ2