Question

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the diagram shows a convex polygon.
what is the value of s?
$s = \square^\circ$

Explanation:

Step1: Recall the exterior angle sum 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 \( 84^\circ \), \( 2s - 38^\circ \), \( s - 21^\circ \), \( 31^\circ \), and \( 3s - 8^\circ \).
So the equation is: \( 84+(2s - 38)+(s - 21)+31+(3s - 8)=360 \)

Step2: Simplify the left - hand side of the equation

First, combine like terms:

• Combine the constant terms: \( 84-38 - 21+31 - 8=(84 + 31)-(38 + 21+8)=115 - 67 = 48 \)
• Combine the \( s \) terms: \( 2s+s + 3s=6s \)

So the equation becomes \( 6s+48 = 360 \)

Step3: Solve for \( s \)

Subtract 48 from both sides of the equation:
\( 6s+48-48=360 - 48 \)
\( 6s=312 \)

Then divide both sides by 6:
\( s=\frac{312}{6}=52 \)

Answer:

\( s = 52^\circ \)