Question

in the adjoining figure abcd is a cyclic quadrilateral find the value of x ​

Answer 1

Step-by-step explanation:

$in \: cyclic \: quadrilateral = > \\ sum \: of \: opposite \: angles \: is \: 180 \\ \\ (2x + 40) + (4x - 64) = 180 \\ 6x - 24 = 180 \\ 6x = 204 \\ x = 34 \\ so \: a = 2x + 40 = 108 \\ and \: b = 4x - 64 = 72$

Answer 2

The value of x=34

Step-by-step explanation:

ABCD is a cyclic quadrilateral

$\angle A=2x+40^{\circ}$

$\angle C=4x-64^{\circ}$

We know that

Sum of opposite angles of cyclic quadrilateral are supplementary.

Therefore,$\angke A+\angle C=180$

Substitute the values then we get

$2x+40+4x-64=180$

$6x-24=180$

$6x=180+24=204$

$x=\frac{204}{6}=34$

The value of x=34

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