Question

the diagram shows a convex polygon.
what is the value of ( v )?
( v = square^circ )

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

$$32^\circ + (v+5)^\circ + (2v-30)^\circ + (2v-47)^\circ + (3v-16)^\circ = 360^\circ$$

Step3: Simplify the left-hand side

Combine like terms:
$$32 + v + 5 + 2v - 30 + 2v - 47 + 3v - 16 = 360$$
$$(v+2v+2v+3v) + (32+5-30-47-16) = 360$$
$$8v - 56 = 360$$

Step4: Solve for $v$

Add 56 to both sides:
$$8v = 360 + 56$$
$$8v = 416$$
Divide by 8:
$$v = \frac{416}{8}$$

Answer:

$52$