the diagram shows a convex polygon. what is the value of y? y = □°

Explanation:

Step1: Recall exterior - angle sum property

The sum of the exterior angles of any convex polygon is 360°.

Step2: Set up an equation

We have the exterior - angle measures (y + 49), (y+40), (y + 37), and (3y). So, ((y + 49)+(y + 40)+(y + 37)+3y=360).

Step3: Combine like - terms

Combining the (y) terms and the constant terms, we get ((1 + 1+1 + 3)y+(49 + 40+37)=360), which simplifies to (6y+126 = 360).

Step4: Isolate the variable term

Subtract 126 from both sides of the equation: (6y=360 - 126), so (6y=234).

Step5: Solve for (y)

Divide both sides by 6: (y=\frac{234}{6}=39).

Answer:

39