Question

find the measure of ∠pft. what is the value of c?

Explanation:

Step1: Note angle - relationship

$\angle PFT$ and the $56^{\circ}$ angle are supplementary (linear - pair of angles).

Step2: Set up the equation

Let $\angle PFT=(3c + 46)^{\circ}$. Since the sum of supplementary angles is $180^{\circ}$, we have $(3c + 46)+56=180$.

Step3: Simplify the left - hand side

$3c+46 + 56=3c + 102$. So, $3c+102 = 180$.

Step4: Solve for $c$

Subtract 102 from both sides: $3c=180 - 102$, $3c = 78$. Then divide both sides by 3: $c=\frac{78}{3}=26$.

Answer:

$26$