Question

which statement regarding the diagram is true?
( mangle wxy = mangle yxz )
( mangle wxy < mangle yzx )
( mangle wxy + mangle yxz = 180^circ )
( mangle wxy + mangle xyz = 180^circ )

Explanation:

Step1: Analyze the diagram's angles

Points W, X, Z are colinear (on a straight line), so \(\angle WXY\) and \(\angle YXZ\) form a linear pair. A linear pair of angles sums to \(180^\circ\).

Step2: Evaluate each option

• Option 1: \(\angle WXY\) is a right angle (from diagram, \(XY\perp WZ\)) and \(\angle YXZ\) is acute, so \(m\angle WXY

eq m\angle YXZ\).

• Option 2: \(\angle WXY = 90^\circ\), \(\angle YZX\) is acute, so \(m\angle WXY>m\angle YZX\), not less.
• Option 3: Since \(\angle WXY\) and \(\angle YXZ\) are a linear pair, \(m\angle WXY + m\angle YXZ = 180^\circ\) (linear pair postulate).
• Option 4: \(\angle WXY\) and \(\angle XYZ\) are not supplementary; their sum is not \(180^\circ\).

Answer:

\(m\angle WXY + m\angle YXZ = 180^\circ\) (the third option)