Question

what is the value of c?

write your answer as an integer or as a decimal rounded to the nearest tenth.

c =

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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, so:
$c + 50 = (5c - 22) + 30$

Step2: Simplify the right-hand side

Combine constant terms on the right:
$c + 50 = 5c + 8$

Step3: Isolate variable terms

Subtract $c$ from both sides:
$50 = 4c + 8$

Step4: Isolate the constant term

Subtract 8 from both sides:
$42 = 4c$

Step5: Solve for $c$

Divide both sides by 4:
$c = \frac{42}{4} = 10.5$

Answer:

$10.5$