Question

Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.
Which statement regarding the diagram is true?

m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°

Answer 1

To analyze the exterior angle formed at point W in triangle XYZ, we can use the properties of exterior angles in triangles. The exterior angle \( \angle WXY \) is formed by extending line segment ZX.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles. Therefore, we have:

\[
m∠WXY = m∠YZX + m∠XYZ
\]

Now, we can evaluate the given statements:

1. **\( m∠WXY = m∠YXZ \)** - This is false. \( m∠YXZ \) is one of the angles inside triangle XYZ.

2. **\( m∠WXY < m∠YZX \)** - This is also false. The exterior angle \( m∠WXY \) is the sum of \( m∠YZX \) and \( m∠XYZ \), so it is greater.

3. **\( m∠WXY + m∠YXZ = 180° \)** - This is false unless the angles WXY and YXZ are supplementary, which they aren't in the triangle context.

4. **\( m∠WXY + m∠XYZ = 180° \)** - This statement is true as \( \angle WXY \) and \( \angle XYZ \) are a linear pair (they make a straight line), and therefore they add up to 180°.

Thus, the true statement regarding the diagram is:

**\( m∠WXY + m∠XYZ = 180° \)**.