Question

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

Explanation:

Step1: Find total interior angles

For a 5-sided polygon, total interior angles are $(5-2)\times180^\circ = 540^\circ$

Step2: Sum all given angles

$$(2u-47^\circ)+(u+39^\circ)+(u+48^\circ)+2u+(u-11^\circ)$$
Simplify: $2u+u+u+2u+u -47+39+48-11 = 7u + 29^\circ$

Step3: Set equal to total, solve for u

$$7u + 29^\circ = 540^\circ$$
$$7u = 540^\circ - 29^\circ = 511^\circ$$
$$u = \frac{511^\circ}{7} = 73^\circ$$

Answer:

$73$