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29 votes
29 votes
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 = (3z + 72)°, find the value of z.
z = 9
z = 12
z = 24
z = 32

User Mhmt
by
3.2k points

2 Answers

15 votes
15 votes

Answer:

z = 12

Explanation:


\boxed{\begin{minipage}{5.4 cm}\underline{Interior angle of a regular polygon}\\\\$(180^(\circ)(n-2))/(n)$\\\\where $n$ is the number of sides.\\\end{minipage}}

Given that the regular polygon has 5 sides, then the measure of one interior angle is:


\implies (180^(\circ)(5-2))/(5)=(180^(\circ)(3))/(5)=(540^(\circ))/(5)=108^(\circ)

If "a" is the measure of one angle, and m∠a = (3z + 72)° then:


\implies m \angle a=108^(\circ)


\implies (3z+72)^(\circ)=108^(\circ)


\implies 3z+72=108


\implies 3z+72-72=108-72


\implies 3z=36


\implies (3z)/(3)=(36)/(3)


\implies z=12

User General Waters
by
2.8k points
15 votes
15 votes

Answer:

  • B) z = 12

===========================

Sum of interior angles of a regular polygon is:

  • S = 180(n - 2), where n- sides of polygon

Find the measure of interior angle a:

  • a = S/5 = 180(5 - 2)/5 = 540/5 = 108

Equate the values of angle a and solve for z:

  • 3z + 72 = 108
  • 3z = 108 - 72
  • 3z = 36
  • z = 12

Correct choice is B.

User Lindy
by
2.7k points