Question

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

Explanation:

Step1: Recall exterior angle sum rule

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

Step2: Sum all given exterior angles

$$20u + (4u+6) + (u+40) + 43 + 10u + 5u + (12u-41) = 360$$

Step3: Simplify the left-hand side

Combine like terms:
$$(20u+4u+u+10u+5u+12u) + (6+40+43-41) = 360$$
$$52u + 48 = 360$$

Step4: Solve for $u$

Subtract 48 from both sides:
$$52u = 360 - 48$$
$$52u = 312$$
Divide by 52:
$$u = \frac{312}{52}$$

Answer:

$u = 6$