A regular polygon is shown, with one of its angle measures labeled a.
9 sided regular polygon with one angle labeled a
If m∠a = (8z + 52)°, find the value of z.
a z = 128
b z = 48
c z = 16
d z = 11
To find the value of z, we need to set up an equation using the given information.
Since a regular polygon has equal interior angles, we can equate the measure of angle a to the total sum of the interior angles divided by the number of sides.
The total sum of the interior angles of a polygon with n sides is (n-2) * 180°.
For a 9-sided polygon, the total sum of the interior angles is (9-2) * 180 = 7 * 180 = 1260°.
So, we have the equation: m∠a = (8z + 52)° = 1260° / 9
Simplifying this equation, we get:
8z + 52 = 140
Subtracting 52 from both sides:
8z = 140 - 52
8z = 88
Dividing both sides by 8:
z = 88 / 8
z = 11
Therefore, the value of z is 11.
Answer: d) z = 11.