Question

if $m\angle yxz = 38$, $m\angle wxz = 19$, and $wz = 8.1$, what is the value of $yw$?

Explanation:

Step1: Identify Angle Bisector

Given \( m\angle YXZ = 38^\circ \) and \( m\angle WXZ = 19^\circ \), we see that \( \angle WXZ=\frac{1}{2}\angle YXZ \). So, \( XW \) bisects \( \angle YXZ \).

Step2: Apply Angle Bisector Theorem (Distance from Angle Bisector)

Since \( XW \) is the angle bisector, and \( YW \perp XY \), \( WZ \perp XZ \), by the Angle Bisector Theorem, the distance from a point on the angle bisector to both sides of the angle is equal. Thus, \( YW = WZ \).

Step3: Substitute Value of \( WZ \)

Given \( WZ = 8.1 \), so \( YW = 8.1 \).

Answer:

8.1