Question

1. which statement does not demonstrate the corollary to the triangle exterior angle theorem? m∠cde > m∠bed m∠cde > m∠dae m∠bed > m∠eda m∠cde > m∠dea

Explanation:

Step1: Recall triangle - exterior - angle theorem

The measure of an exterior angle of a triangle is greater than the measure of either non - adjacent interior angle.

Step2: Analyze each option

In \(\triangle ADE\), \(\angle CDE\) is an exterior angle. By the triangle exterior - angle theorem, \(m\angle CDE>m\angle DAE\) and \(m\angle CDE > m\angle DEA\). In \(\triangle BED\), \(\angle BED\) is an interior angle and there is no direct relation based on the exterior - angle theorem between \(\angle BED\) and \(\angle CDE\) that can be derived from the given figure.

Answer:

C. \(m\angle BED>m\angle EDA\)