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 = (5z + 65)°, find the value of z.
a) z = 15
b) z = 20
c) z = 23
d) z = 41
To find the value of z, we need to set up an equation using the given information. Since we know that the sum of the interior angles of a 9-sided regular polygon is 180 * (9 - 2) = 1260 degrees, we can set up the equation:
m∠a = (5z + 65)°
Since a regular polygon has all equal angles, the measure of each angle can be found by dividing the sum of the angles by the number of angles. In this case, we have:
m∠a = 1260/9 = 140°
Setting this equal to the expression (5z + 65):
140 = 5z + 65
Subtracting 65 from both sides:
75 = 5z
Dividing both sides by 5:
z = 15
Therefore, the value of z is 15.
Answer: a) z = 15