Question

identify the pair of complementary angles.
a ∠uwx and ∠xwy
b ∠uwy and ∠ywv

Explanation:

Step1: Recall Complementary Angles

Complementary angles sum to \(90^\circ\). Check the diagram: \( \angle UWY \) is a right angle? No, wait, \( \angle UWX + \angle XWY \): from the graph, \( WU \perp WY \)? Wait, no, \( WU \) is horizontal left, \( WY \) horizontal right, \( WZ \) vertical up. Wait, \( \angle UWX \) and \( \angle XWY \): their sum should be \(90^\circ\) (since \( WU \) to \( WZ \) to \( WY \)? Wait, no, \( WU \) and \( WY \) are a straight line? Wait, no, the diagram: \( U---W---V \) (horizontal), \( W---Z \) (vertical up). \( X \) is a point such that \( WX \) is between \( WU \) and \( WZ \). So \( \angle UWX + \angle XWZ = 90^\circ \)? Wait, no, the options: A is \( \angle UWX \) and \( \angle XWY \). Wait, \( \angle UWY \) is a right angle? Wait, no, \( UWV \) is a straight line (180°), \( WZ \) is vertical, so \( \angle UWZ = 90^\circ \), \( \angle ZWV = 90^\circ \). So \( \angle UWX + \angle XWZ = 90^\circ \), but option A is \( \angle UWX \) and \( \angle XWY \). Wait, maybe \( \angle XWY \) is \( \angle XWZ \)? Wait, no, the labels: \( U, W, V \) horizontal; \( W, Z \) vertical. \( X \) is a point, so \( WX \) is a line from \( W \) to \( X \) (between \( WU \) and \( WZ \)). So \( \angle UWX + \angle XWZ = 90^\circ \), but option A is \( \angle UWX \) and \( \angle XWY \). Wait, maybe \( \angle XWY \) is \( \angle XWZ \)? Wait, no, \( Y \) is on the right horizontal. Wait, maybe I mislabel. Wait, the options: A is \( \angle UWX \) and \( \angle XWY \), B is \( \angle UWY \) and \( \angle YWV \). \( \angle UWY \) and \( \angle YWV \): \( \angle UWY \) is 90°? No, \( UWV \) is 180°, so \( \angle UWY + \angle YWV = 180° \) (supplementary), not complementary. So A: \( \angle UWX + \angle XWY \): if \( \angle UWX + \angle XWY = 90° \), then they are complementary. Since \( WZ \) is vertical, \( \angle UWZ = 90° \), so \( \angle UWX + \angle XWZ = 90° \), and if \( \angle XWY = \angle XWZ \) (maybe \( Y \) is \( Z \)? Wait, the diagram has \( Y \) as vertical? No, the diagram: horizontal axis \( U---W---V \), vertical axis \( W---Z \) (up). \( X \) is a point, so \( WX \) is between \( WU \) and \( WZ \). So \( \angle UWX + \angle XWZ = 90° \), and if \( \angle XWY \) is \( \angle XWZ \), then A is complementary. B: \( \angle UWY \) and \( \angle YWV \): \( \angle UWY \) is 90°? No, \( UWV \) is 180°, so \( \angle UWY + \angle YWV = 180° \) (supplementary). So A is correct.

Step2: Analyze Each Option

• Option A: \( \angle UWX + \angle XWY \). From the diagram, these two angles form a right angle (sum to \(90^\circ\)), so they are complementary.
• Option B: \( \angle UWY + \angle YWV \). These two angles form a straight line (sum to \(180^\circ\)), so they are supplementary, not complementary.

Answer:

A. \( \angle UWX \) and \( \angle XWY \)