Question

what is the value of c?
diagram: points u, v, t, s with right angles at t (on ut) and v (on uv), segments st labeled ( c + 60 ) and sv labeled ( 4c ), angle at u bisected by us
( c = square )

Explanation:

Step1: Recognize Angle Bisector Property

Since \( SU \) is an angle bisector, and \( ST \perp UT \), \( SV \perp UV \), by the Angle Bisector Theorem (or the property that the distances from a point on an angle bisector to the sides of the angle are equal), we have \( ST = SV \). So \( c + 60 = 4c \).

Step2: Solve for \( c \)

Subtract \( c \) from both sides: \( 60 = 4c - c \), which simplifies to \( 60 = 3c \). Then divide both sides by 3: \( c=\frac{60}{3}=20 \).

Answer:

\( 20 \)