Question

27. In the figure ABCD is a cyclic quadrilateral. Its opposite angles are
(4x - y) and (2x + y) & (x + 2y) and (-x+8y)
Find the measures of angles of quadrilateral​

Answer 1

Answer:

Given opposite angles are= (4x-y),(2x+y),and (X+2y)(-x+8y)

We know that sum opposite angles of a cyclic quadrilateral is 180°

So,

4x-y+2x+y=180

6y=180

y= 30

Also

x+2y-x+8y=180

2x+10y=180

X+5y=90.....(1)

Now putting The value of y =30

equation (1)

We get

\begin{gathered}x + 5y = 180 \\ \\ x = 180 - 150 \\ \\ x = 30\end{gathered}x+5y=180x=180−150x=30

So now bye putting the value of x and y we can find the measure of angles which are as follows

1) 4x-30=4×30-30=120-30=90°

2)2x+y=2×30+30=60+30=90°

3)X+2y=30+2×30=30+60=90°

4)-x+8y=-30+8×30=-30+240=210°

But there is an error because the 4th angle can't be more then 90° 

because the sum of all angles of an quadrilateral is 360°

Make correction of u r question

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