Question

what is $m\angle d$? enter your answer in the box.

Explanation:

Step1: Find ∠AEB

In triangle \( AEB \), the sum of angles is \( 180^\circ \). Given \( \angle A = 14^\circ \) and \( \angle B = 45^\circ \), so \( \angle AEB = 180^\circ - 14^\circ - 45^\circ = 121^\circ \).

Step2: Find ∠CED

\( \angle AEB \) and \( \angle CED \) are vertical angles, so \( \angle CED = \angle AEB = 121^\circ \).

Step3: Find \( m\angle D \)

In triangle \( CED \), the sum of angles is \( 180^\circ \). Given \( \angle C = 27^\circ \) and \( \angle CED = 121^\circ \), so \( m\angle D = 180^\circ - 27^\circ - 121^\circ = 32^\circ \).

Answer:

\( 32^\circ \)