ABCD is a cyclic quadrilateral. Find the value of y .

The correct answer is Option (3) → 64°

In a cyclic quadrilateral, opposite angles add up to 180°. The 116° at D lies outside the quadrilateral, on the extended line AD, so find the inside angle at D first.

• Angles on a straight line: \(\angle ADC=180^\circ-116^\circ=64^\circ\)

• Opposite angles B and D: \(\angle ABC=180^\circ-64^\circ=116^\circ\)

• \(\angle ABC\) is made up of \(y\) and 52°: \(y=116^\circ-52^\circ=64^\circ\)

Tip: An exterior angle of a cyclic quadrilateral equals the interior opposite angle, so \(\angle ABC=116^\circ\) can be read straight off the figure.