Question

quadrilateral defg is inscribed in circle h. what is the relationship between m∠d and m∠f? m∠d + m∠f = 90°; m∠d + m∠f = 180°; m∠d = m∠f; 2m∠d = m∠f

Explanation:

Step1: Recall cyclic quadrilateral property

A cyclic quadrilateral (a quadrilateral inscribed in a circle) has the property that the sum of the measures of its opposite angles is \(180^\circ\).

Step2: Identify opposite angles

In quadrilateral \(DEFG\) inscribed in circle \(H\), \(\angle D\) and \(\angle F\) are opposite angles.

Step3: Apply the property

Using the property of cyclic quadrilaterals, we get \(m\angle D + m\angle F = 180^\circ\).

Answer:

\(m\angle D + m\angle F = 180^\circ\) (the option with this equation)