Question

1. given ∠aeb = ∠dec prove ∠aec = ∠deb

Explanation:

Step1: Define the angle - addition relationship

We know that \(\angle AEC=\angle AEB+\angle BEC\) and \(\angle DEB = \angle DEC+\angle BEC\).

Step2: Use the given condition

Since \(\angle AEB=\angle DEC\) (given), we can substitute \(\angle AEB\) for \(\angle DEC\) in the expression for \(\angle DEB\). So, \(\angle DEB=\angle AEB + \angle BEC\).

Step3: Compare with \(\angle AEC\)

Because \(\angle AEC=\angle AEB+\angle BEC\) and \(\angle DEB=\angle AEB + \angle BEC\), we can conclude that \(\angle AEC=\angle DEB\).

Answer:

\(\angle AEC=\angle DEB\) is proved as shown above.