Question

ABCD is a cyclic quadilateral such that $\angle$B = 5 $\angle$D and $\angle$C = 3 $\angle$A. Find the measure of each angle of the quadilateral.

Answer 1

In a cyclic quadrilateral, the sum of opposite angles = 180 degress.
$\to$ A + C = 180 and B + D = 180
$\to$ A + 3A = 180 $\to$ A = 45 degrees and B = 135 degrees.
$\to$ 5D + D = 180 $\to$ D = 30 and B = 150 degrees