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 = (2z + 54)°, find the value of z.
a) z = 63
b) z = 9
c) z = 18
d) z = 27
Since it is a regular polygon, all of its angles are congruent. Therefore, each angle measures (2z + 54)°.
For a 5-sided regular polygon, the sum of its interior angles can be found using the formula:
Sum of angles = (n - 2) * 180°,
where n is the number of sides.
Substituting n = 5, we have:
Sum of angles = (5 - 2) * 180° = 3 * 180° = 540°.
Since the polygon is regular, each angle is congruent, so we can find the measure of each angle by dividing the sum of angles by the number of sides:
Each angle = Sum of angles / number of sides = 540° / 5 = 108°.
Therefore, (2z + 54)° = 108°.
To find z, we need to solve the equation:
2z + 54 = 108.
Simplifying the equation:
2z = 108 - 54,
2z = 54,
z = 27.
Therefore, the value of z is 27.
Answer: d) z = 27