Question

two opposite angles of parallelogram are (4x+3) and (57+2x) .find all angle of a parallelogram. (please answer it step by step instructions)​

Answer 1

since, the opposite angles of parallelogram are equal,

So,

$4x + 3 = 57 + 2x$

$4x - 2x = 57 - 3 =$

$2x = 54$

$x = \frac{54}{2} = 27$

Putting the value of x in the angle,

$(4 \times 27) + 3 = 108 + 3 = {111}^{o}$

Therefore, two opposite angles of parallelogram is 111 degree.

Since, Remaining two angles are also equal,

So, Let those angles be x degree each.

Now,

$111 + x + 111 + x = {360}^{o}$

$2x = 360 - 222 = {138}^{o}$

$x = \frac{138}{2} = {69}^{o}$

Therefore, the angles are 111, 69, 111, 69

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