Question

prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180 degree using the above find X and Y . Pls do it fast the equations are x+y,2x,5x-y and x+2y first fig

Answer 1

PS: the figure is not clear

u can solve it by adding the opp angle nd equating to 180

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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 =

So, sum of opposite angles become

Now, in the question,

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

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

As given in figure

x+2y+2x = 180

3x+2y =180 ..........(1)

5y-x+x+y = 180

6y=180

y=30 ............(2)

Putting value of y in (1)

3x+ 60 =180

3x = 120

x= 40

The value of x=40° and y=30°.

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