Question

Triangle Z Y X is shown with its exterior angles. Point Z extends to point L, point X extends to point N, and point Y extends to point M.
Analyze the diagram to complete the statements.

The m∠MXN is
the m∠YZX.

The m∠LZX is
the m∠ZYX + m∠YXZ.

The m∠MYL is
180° − m∠ZYX.

Answer 1

Based on the provided information regarding triangle \( ZYX \) and its exterior angles, we can analyze the relationships and complete the statements as follows:

1. The exterior angle \( \angle MXN \) is equal to the sum of the two opposite interior angles. Therefore, we have:
\[
\text{The } m\angle MXN \text{ is equal to } m\angle YZX.
\]

2. The exterior angle \( \angle LZX \) at vertex \( Z \) is equal to the sum of the interior angles at vertices \( Y \) and \( X \). Thus, we express it as:
\[
\text{The } m\angle LZX \text{ is equal to } m\angle ZYX + m\angle YXZ.
\]

3. The exterior angle \( \angle MYL \) at vertex \( Y \) can be expressed as the supplement to the interior angle at vertex \( Y \). Therefore, we get:
\[
\text{The } m\angle MYL \text{ is } 180° - m\angle ZYX.
\]

Combining these results gives us the finalized statements pertaining to the relationships among the angles in triangle \( ZYX \) and its exterior angles.