Question

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

Answer 1

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`

Answer 2

• 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.