A regular polygon is shown with one of its angle measures labeled a.
5 sided regular polygon with one angle labeled a
If m∠a = (4z + 32)°, find the value of z.
a z = 8
b z = 15
c z = 19
d z = 37
To find the value of z, we need to set up an equation using the given information.
Since it is a regular polygon, all of its angles are equal. Therefore, we can set up the equation:
m∠a = (4z + 32)° = 180° / (n-2)
where n is the number of sides of the polygon.
In this case, the polygon has 5 sides, so we can substitute n = 5 into the equation:
(4z + 32)° = 180° / (5-2)
(4z + 32)° = 180° / 3
(4z + 32)° = 60°
Now we can solve for z:
4z + 32 = 60
4z = 60 - 32
4z = 28
z = 28/4
z = 7
Therefore, the value of z is 7. None of the given options (a, b, c, d) match the result.