Question

what value of x makes the given parallelogram a square

Answer 1

As we know angle subtended by any side at center is 90 for square

So 13 x +55 = 90

13x = 35

x = 35/13 = 2.69

Answer 2

$since \: the \: diagonals \: of \: square \: intersect \: at \: 90 \\ for \: the \: above \: parrallelogram \: to \: be \: a \: square \: 13x + 5.5 \: must \: be \: equal \: to \: 90 \\ 13x + 5.5 = 90 \\ 13x = 84.5 \\ x = 6.5$