Question

A pentagon has 5 sides, and one angle of a regular pentagon measures (4w + 7)°. Determine the value of w. Round to the nearest whole number.

a) w = 108
b) w = 43
c) w = 29
d) w = 25

Answer 1

The value of w is approximately 25.

Therefore, the correct answer is: option d) w = 25

Step-by-step explanation:

To find the value of w, we need to solve the equation (4w + 7)° = 180° - 360° / 5.

This is because the sum of the angles in a regular pentagon is 180°, and each angle in a regular pentagon is equal.

Simplifying the equation, we get:

4w + 7 = 108.

Subtracting 7 from both sides, we have:

4w = 101.

Dividing both sides by 4, the value of w is approximately 25.