Question

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

Explanation:

Step1: Recall exterior angle sum rule

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

Step2: Sum all given exterior angles

$$(y+9)+(2y-46)+(y+43)+y+(y+42) = 360$$

Step3: Simplify the left-hand side

Combine like terms:
$$y+2y+y+y+y + 9-46+43+42 = 360$$
$$6y + 48 = 360$$

Step4: Solve for $y$

Subtract 48 from both sides:
$$6y = 360 - 48$$
$$6y = 312$$
Divide by 6:
$$y = \frac{312}{6}$$

Answer:

$52$