Question

if $m\angle yxw = 21$, $yw = 5$, and $wz = 5$, what is $m\angle zxy$?

Explanation:

Step1: Identify the Angle Bisector

Since \( YW \perp XY \), \( WZ \perp XZ \) (right angles), and \( YW = WZ = 5 \), by the Angle Bisector Theorem (a point equidistant from the sides of an angle lies on the angle bisector), \( XW \) bisects \( \angle ZXY \).

Step2: Calculate \( m\angle ZXY \)

Given \( m\angle YXW = 21^\circ \), and \( XW \) bisects \( \angle ZXY \), so \( m\angle ZXY = 2 \times m\angle YXW \).
Substitute \( m\angle YXW = 21^\circ \): \( m\angle ZXY = 2\times21^\circ = 42^\circ \).

Answer:

42°