Question

c.6 angle bisectors
if ux = wx = 17, m∠uvx = y + 54°, and m∠wvx = 4y, what is the value of y?
y = \boxed{^\circ}

Explanation:

Step1: Identify Angle Bisector

Since \( UX = WX = 17 \) and \( \angle WVX \) and \( \angle UVX \) are related by the angle bisector (as \( XW \perp WV \) and \( XU \perp VU \), so \( VX \) bisects \( \angle WVU \)), thus \( m\angle UVX = m\angle WVX \).

Step2: Set Up Equation

Set \( y + 54^\circ = 4y \).

Step3: Solve for \( y \)

Subtract \( y \) from both sides: \( 54^\circ = 3y \).
Divide by 3: \( y=\frac{54^\circ}{3}=18^\circ \).

Answer:

\( 18 \)