Question

1. which statement does not demonstrate the corollary to the triangle exterior angle theorem? m∠x > m∠e m∠y > m∠e m∠x > m∠y m∠y > m∠f

Explanation:

Step 1: 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. In the given triangle, $\angle x$ and $\angle y$ are exterior angles. $\angle x$ is an exterior angle with non - adjacent interior angles $\angle e$ and $\angle c$, and $\angle y$ is an exterior angle with non - adjacent interior angles $\angle e$ and $\angle f$. So, $m\angle x>m\angle e$, $m\angle x > m\angle c$, $m\angle y>m\angle e$, and $m\angle y>m\angle f$.

Step 2: Analyze each option

Option 1: $m\angle x>m\angle e$ follows the triangle exterior - angle theorem. Option 2: $m\angle y>m\angle e$ follows the triangle exterior - angle theorem. Option 3: $m\angle x>m\angle y$ is not a consequence of the triangle exterior - angle theorem. Option 4: $m\angle y>m\angle f$ follows the triangle exterior - angle theorem.

Answer:

$m\angle x > m\angle y$