Question

what is the value of c?

c = \square^\circ

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Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
$\boldsymbol{c+45^\circ=(c-31^\circ)+(c-26^\circ)}$

Step2: Simplify right-hand side

Combine like terms on the right.
$c+45^\circ=2c-57^\circ$

Step3: Solve for c

Isolate c by rearranging terms.
$45^\circ+57^\circ=2c-c$
$102^\circ=c$

Answer:

$102$