Final answer:
The value of w in the angle expression for a regular pentagon is found by setting (4w+7)° equal to 108 degrees and solving for w, which when rounded to the nearest whole number, gives w = 25.
Step-by-step explanation:
The question involves finding the measure of an interior angle in a regular pentagon.
In a regular pentagon, all sides and angles are equal, and the sum of the internal angles is (5-2) times 180 degrees, which is 540 degrees. Since there are five angles in a regular pentagon, each angle measures 540 ÷ 5 = 108 degrees.
To find the value of w, we set up the equation based on the angle expression given as (4w+7)° and equal it to the measure of each angle in the pentagon, which is 108 degrees. Therefore, we have:
4w + 7 = 108
Now, we solve for w:
4w = 108 - 7
w = 101 ÷ 4
w = 25.25
When we round w to the nearest whole number, we get w = 25.