Question

triangle xyz is a right triangle with the right angle at vertex y. angle x must be dropdown. angle z must be dropdown. the sum of angles x and z must be dropdown 90°.

Explanation:

Step1: Recall triangle angle sum

Sum of angles in triangle: $180^\circ$.

Step2: Identify right angle

Right angle at Y: $\angle Y = 90^\circ$.

Step3: Calculate sum of X and Z

$\angle X + \angle Z = 180^\circ - 90^\circ = 90^\circ$.

Step4: Determine type of X and Z

Angles X and Z are acute (less than $90^\circ$).

Answer:

Angle X must be: acute
Angle Z must be: acute
The sum of angles X and Z must be: equal to
(Note: Assuming dropdown options include "acute" for the first two blanks and "equal to" for the third blank, as standard for such problems.)