Question

quadrilateral cdef is a kite. what is m∠f?

m∠f = \boxed{\circ}

Explanation:

Step1: Recall Kite Angle Sum

A kite is a quadrilateral, so the sum of its interior angles is \( (4 - 2) \times 180^\circ = 360^\circ \).

Step2: Identify Equal Angles in Kite

In a kite, one pair of opposite angles (between the unequal sides) are equal. Here, \( \angle C = 138^\circ \), \( \angle E = 114^\circ \), and \( \angle D = \angle F \) (since the marked sides suggest \( CD = CF \) and \( DE = FE \), so the angles opposite those sides: \( \angle D \) and \( \angle F \) are equal).

Step3: Calculate Sum of Known Angles

Sum of \( \angle C \) and \( \angle E \): \( 138^\circ + 114^\circ = 252^\circ \).

Step4: Find Sum of Remaining Angles

Subtract from total: \( 360^\circ - 252^\circ = 108^\circ \). This is the sum of \( \angle D \) and \( \angle F \).

Step5: Find \( m\angle F \)

Since \( \angle D = \angle F \), divide by 2: \( \frac{108^\circ}{2} = 54^\circ \).

Answer:

\( 54 \)