Question

the diagram shows a convex polygon. what is the value of s? s = \boxed{\space}^\circ

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 angles are \( 2s - 44^\circ \), \( 30^\circ \), \( 129^\circ \), \( 2s - 42^\circ \), \( 33^\circ \), \( s - 3^\circ \), \( 2s - 2^\circ \).
So the equation is: \( (2s - 44)+30 + 129+(2s - 42)+33+(s - 3)+(2s - 2)=360 \)

Step2: Combine like terms

First, combine the \( s \) terms: \( 2s+2s+s+2s = 7s \)
Then combine the constant terms: \( - 44+30 + 129-42+33-3-2 \)
Calculate the constant sum: \( (-44 - 42-3 - 2)+(30 + 129+33)=(-91)+(192) = 101 \)
So the equation becomes: \( 7s+101 = 360 \)

Step3: Solve for \( s \)

Subtract 101 from both sides: \( 7s=360 - 101=259 \)
Divide both sides by 7: \( s=\frac{259}{7} = 37 \)

Answer:

\( 37 \)