Question

what are the values of b and c?
v
b
u
4
74°
t
b =
c =

Explanation:

Step1: Identify congruent - sides

Since the two - triangle sharing side $SU$ have equal - length markings on the other two pairs of sides, $\triangle VUS\cong\triangle TUS$ (by SSS congruence criterion). So, $b = 4$ (corresponding sides of congruent triangles are equal).

Step2: Calculate angle $c$

In $\triangle TUS$, we know one angle is $74^{\circ}$. Since $\triangle VUS\cong\triangle TUS$, and considering the angle - bisecting property (from the congruence), $c=\frac{74^{\circ}}{2}=37^{\circ}$.

Answer:

$b = 4$, $c = 37^{\circ}$