Question

question 4 (3 points)
δxyz, m∠x = 100° and m∠y = 50°. list the sides in order from smallest to largest.
(only write the two letters that represent each side)
smallest side:
medium side:
largest side:
blank 1:
blank 2:
blank 3:

Explanation:

Step1: Find the measure of angle \( Z \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( m\angle Z=180 - 100 - 50=30^{\circ} \).

Step2: Recall the side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.

• Side opposite \( \angle Z\) (smallest angle) is \( XY\).
• Side opposite \( \angle Y\) (medium - sized angle) is \( XZ\).
• Side opposite \( \angle X\) (largest angle) is \( YZ\).

Answer:

smallest side: \( XY\)
medium side: \( XZ\)
largest side: \( YZ\)