the diagram shows a convex polygon.\nwhat is the value of y?\n$y = \\square^\\circ$

Explanation:

Step1: Recall exterior angle sum rule

For any convex polygon, the sum of all exterior angles is $360^\circ$.

Step2: Set up the equation

Add all given exterior angles: $62^\circ + 41^\circ + 37^\circ + 2y + 2y = 360^\circ$

Step3: Simplify the left side

Combine like terms and constants: $140^\circ + 4y = 360^\circ$

Step4: Isolate the variable term

Subtract $140^\circ$ from both sides: $4y = 360^\circ - 140^\circ = 220^\circ$

Step5: Solve for y

Divide both sides by 4: $y = \frac{220^\circ}{4}$

Answer:

$55^\circ$