Question

what are m∠d and m∠e?
m∠d = \boxed{\circ}
m∠e = \boxed{\circ}

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\).
For \(\angle F\) and \(\angle D\), we have \(m\angle F + m\angle D=180^{\circ}\).
Given \(m\angle F = 68^{\circ}\), then \(m\angle D=180^{\circ}- 68^{\circ}\).

Step2: Calculate \(m\angle D\)

\(m\angle D = 112^{\circ}\)
For \(\angle G\) and \(\angle E\), we have \(m\angle G + m\angle E=180^{\circ}\).
Given \(m\angle G = 98^{\circ}\), then \(m\angle E=180^{\circ}-98^{\circ}\)

Step3: Calculate \(m\angle E\)

\(m\angle E = 82^{\circ}\)

Answer:

\(m\angle D = 112^{\circ}\), \(m\angle E = 82^{\circ}\)