Question

what is the measure of ∠xyz?
diagram: two rays from point y, labeled x (upper) and z (lower), forming an angle
a 120° (selected with a blue dot)
b 90°
c 180°
d 30°

Explanation:

Step1: Analyze the angle type

The angle ∠XYZ is formed by two rays from a common vertex Y. Visually, it's a small acute - like angle (though we can also reason about typical angle measures). A 120° is obtuse, 90° is right, 180° is straight. The angle between the two rays looks like a 30° angle (a small angle between two non - perpendicular, non - straight, non - large obtuse rays).

Step2: Eliminate incorrect options

• Option A: 120° is an obtuse angle, the angle in the diagram is not obtuse, so eliminate A.
• Option B: 90° is a right angle (L - shaped), the angle here is not right - angled, so eliminate B.
• Option C: 180° is a straight angle (a straight line), the angle here is not a straight line, so eliminate C.
• Option D: 30° is a small acute angle which matches the visual of the angle between the two rays.

Answer:

D. 30°