Question

the diagram shows a triangle. what is the value of c?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. So, we have the equation $20c + 17c+106 = 180$.

Step2: Combine like - terms

Combining the terms with $c$ on the left - hand side, we get $(20 + 17)c+106=180$, which simplifies to $37c+106 = 180$.

Step3: Isolate the term with $c$

Subtract 106 from both sides of the equation: $37c=180 - 106$. So, $37c = 74$.

Step4: Solve for $c$

Divide both sides of the equation by 37: $c=\frac{74}{37}$. Thus, $c = 2$.

Answer:

$2$