Question

find the value of c.
(4c + 4)°
(c + 52)°

Explanation:

Step1: Identify angle - relationship

The two angles $(4c + 4)^{\circ}$ and $(c + 52)^{\circ}$ are vertical angles, and vertical angles are equal. So we set up the equation $4c+4=c + 52$.

Step2: Solve the equation for c

Subtract c from both sides: $4c - c+4=c - c + 52$, which simplifies to $3c+4 = 52$. Then subtract 4 from both sides: $3c+4 - 4=52 - 4$, getting $3c=48$. Divide both sides by 3: $\frac{3c}{3}=\frac{48}{3}$, so $c = 16$.

Answer:

$16$