Question

1. consider the diagram. calculate the value of x. (diagram of a cyclic quadrilateral with angles 72° and 116° marked)

Explanation:

Step1: Identify cyclic quadrilateral property

Opposite angles sum to $180^\circ$.

Step2: Calculate $y$ first

$y + 116^\circ = 180^\circ \implies y = 180 - 116 = 64^\circ$.

Step3: Use triangle angle sum for $x$

Triangle angles: $72^\circ, y=64^\circ, x$. Sum is $180^\circ$.
$x = 180 - 72 - 64 = 44^\circ$.

Answer:

44