Question

for exercise 17, select all that apply. 17. select all the statements that accurately describe the triangles shown. (lesson 7) a b 57° 75° c z 48° 57° x y a. m∠c = 48° b. m∠y = 75° c. m∠c = m∠x d. △abc is similar to △xyz e. △abc is congruent to △xyz

Explanation:

Step1: Find angle C in △ABC

The sum of angles in a triangle is 180°. So, $m\angle C=180^{\circ}-(57^{\circ} + 75^{\circ})=48^{\circ}$.

Step2: Analyze each option

• Option A: Since $m\angle C = 48^{\circ}$, this option is correct.
• Option B: In △XYZ, we know two angles are 48° and 57°. So $m\angle Y=180^{\circ}-(48^{\circ}+57^{\circ}) = 75^{\circ}$, this option is correct.
• Option C: $m\angle C = 48^{\circ}$ and $m\angle X=57^{\circ}$, so $m\angle C

eq m\angle X$, this option is incorrect.

• Option D: The angles of △ABC are 57°, 75°, 48° and the angles of △XYZ are 57°, 75°, 48°. Since the corresponding angles are equal, △ABC is similar to △XYZ, this option is correct.
• Option E: There is no information about side - lengths. Just having equal angles means similarity not congruence, this option is incorrect.

Answer:

A. $m\angle C = 48^{\circ}$, B. $m\angle Y = 75^{\circ}$, D. $\triangle ABC$ is similar to $\triangle XYZ$