Question

8 triangle xyz is shown.

image of triangle xyz with angle at x: 40°, angle at z: 100°

which triangle must be similar to triangle xyz?

a a triangle with two angles that measure 40°
b a triangle with angles that measure 40° and 60°
partially visible option c

Explanation:

Step1: Find angle Y in XYZ

In triangle \( XYZ \), the sum of angles in a triangle is \( 180^\circ \). Given \( \angle X = 40^\circ \) and \( \angle Z = 100^\circ \), so \( \angle Y = 180^\circ - 40^\circ - 100^\circ = 40^\circ \). So angles of \( XYZ \) are \( 40^\circ \), \( 40^\circ \), \( 100^\circ \).

Step2: Analyze Option A

A triangle with two angles \( 40^\circ \). The third angle would be \( 180 - 40 - 40 = 100^\circ \). So its angles are \( 40^\circ \), \( 40^\circ \), \( 100^\circ \), same as \( XYZ \). By AA similarity, they are similar.

Step3: Analyze Option B

A triangle with angles \( 40^\circ \) and \( 60^\circ \). Third angle is \( 180 - 40 - 60 = 80^\circ \). Angles don't match \( XYZ \), so not similar.

Answer:

A. a triangle with two angles that measure \( 40^\circ \)