Question

what is the value of c?
there is a triangle with angles labeled as $c + 5^circ$, $c - 42^circ$, and an exterior angle labeled as $c + 36^circ$. find the value of $c$.
$c = \square ^\circ$

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$c+36 = (c-42) + (c+5)$$

Step2: Simplify right-hand side

Combine like terms on the right:
$$c+36 = 2c - 37$$

Step3: Isolate variable c

Subtract $c$ and add 37 to both sides:
$$36 + 37 = 2c - c$$
$$73 = c$$

Answer:

$73$