Question

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

Explanation:

Step1: Find total interior angles

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

Step2: Sum all given angles

$112 + (4v-38) + 4v + 2v + (3v+37) = 540$

Step3: Simplify the left side

Combine like terms:
$112 - 38 + 37 + 4v + 4v + 2v + 3v = 540$
$111 + 13v = 540$

Step4: Solve for $v$

Subtract 111 from both sides:
$13v = 540 - 111 = 429$
Divide by 13:
$v = \frac{429}{13} = 33$

Answer:

$v = 33^\circ$