Question

calculate the size of angle edc.

Explanation:

Step1: Find angle \( BCA \)

Since \( AB = AC \), triangle \( ABC \) is isosceles. The exterior angle at \( B \) is \( 133^{\circ} \), so the interior angle \( \angle ABC=180 - 133=47^{\circ} \). Then \( \angle BCA=(180-(47 + 47))\div1 = 86^{\circ} \) (sum of angles in a triangle is \( 180^{\circ} \)).

Step2: Find angle \( DCF \)

We know that \( \angle BCD = 126^{\circ} \) and \( \angle FCE = 101^{\circ} \). The sum of angles around point \( C \) is \( 360^{\circ} \). So \( \angle DCF=360-(126 + 86+101)=47^{\circ} \)

Step3: Use the property of parallelogram ( \( AC = DE \), \( AC\parallel DE \), \( CD = AE \), \( CD\parallel AE \))

Since \( AC = DE \) and \( AC\parallel DE \), \( CD = AE \) and \( CD\parallel AE \), \( ACDE \) is a parallelogram. In parallelogram \( ACDE \), \( \angle EDC=\angle CAE \) (alternate - interior angles property for parallel lines \( CD\parallel AE \) and transversal \( AC \)). Also, \( \angle CAE = 180-(47 + 62)=71^{\circ} \) (sum of angles on a straight line \( AFE \) is \( 180^{\circ} \))

Answer:

\( 71^{\circ} \)