Answer:
[tex]x=85\\ \\y=100\\ \\z=100[/tex]
Step-by-step explanation:
Angles with measures of [tex]95^{\circ}[/tex] and [tex]x^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]
[tex]x+95=180\\ \\x=180-95\\ \\x=85[/tex]
Angles with measures of [tex]80^{\circ}[/tex] and [tex]y^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]
[tex]y+80=180\\ \\y=180-80\\ \\y=100[/tex]
Find the measures of two remaining interior angles of the pentagon:
[tex]1. \ 180^{\circ}-62^{\circ}=118^{\circ}\\ \\2.\ 180^{\circ}-53^{\circ}=127^{\circ}[/tex]
The sum of the measures of all interior angles in the pentagon is
[tex](5-2)\cdot 180^{\circ}=540^{\circ},[/tex]
then
[tex]95^{\circ}+118^{\circ}+100^{\circ}+z^{\circ}+127^{\circ}=540^{\circ}\\ \\440^{\circ}+z^{\circ}=540^{\circ}\\ \\z^{\circ}=100^{\circ}[/tex]
