Answer:
z = 12
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Interior angle of a regular polygon}\\\\$\dfrac{180^{\circ}(n-2)}{n}$\\\\where $n$ is the number of sides.\\\end{minipage}}[/tex]
Given that the regular polygon has 5 sides, then the measure of one interior angle is:
[tex]\implies \dfrac{180^{\circ}(5-2)}{5}=\dfrac{180^{\circ}(3)}{5}=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
If "a" is the measure of one angle, and m∠a = (3z + 72)° then:
[tex]\implies m \angle a=108^{\circ}[/tex]
[tex]\implies (3z+72)^{\circ}=108^{\circ}[/tex]
[tex]\implies 3z+72=108[/tex]
[tex]\implies 3z+72-72=108-72[/tex]
[tex]\implies 3z=36[/tex]
[tex]\implies \dfrac{3z}{3}=\dfrac{36}{3}[/tex]
[tex]\implies z=12[/tex]
