Question

what is the value of c?
there is a triangle in the diagram, with one exterior angle labeled as ( c + 43^circ ), and two interior angles labeled as ( c - 10^circ ) and ( c + 8^circ ). we need to find the value of ( c ).

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$c + 43^\circ = (c - 10^\circ) + (c + 8^\circ)$

Step2: Simplify right-hand side

Combine like terms on the right:
$c + 43^\circ = 2c - 2^\circ$

Step3: Isolate variable c

Subtract $c$ and add $2^\circ$ to both sides:
$43^\circ + 2^\circ = 2c - c$

Answer:

$45$