Question

the diagram shows a convex polygon.
what is the value of c?
c = \boxed{\space}°

Explanation:

Step1: Recall the sum of exterior angles of a convex polygon.

The sum of the exterior angles of any convex polygon is \(360^\circ\). So we add up all the given exterior angles and set the sum equal to \(360^\circ\).
The exterior angles are \(3c - 43^\circ\), \(c - 20^\circ\), \(c - 20^\circ\), \(c\), and \(2c + 35^\circ\).
So the equation is: \((3c - 43)+(c - 20)+(c - 20)+c+(2c + 35)=360\)

Step2: Combine like terms.

First, expand the left - hand side:
\(3c-43 + c-20 + c-20 + c+2c + 35=360\)
Combine the \(c\) terms: \(3c + c + c + c+2c=(3 + 1+1 + 1+2)c = 8c\)
Combine the constant terms: \(-43-20 - 20+35=-43-(20 + 20)+35=-43 - 40+35=-48\)
So the equation becomes \(8c-48 = 360\)

Step3: Solve for \(c\).

Add 48 to both sides of the equation:
\(8c-48 + 48=360 + 48\)
\(8c=408\)
Divide both sides by 8:
\(c=\frac{408}{8}=51\)

Answer:

\(51\)