Question

Only need help on these last problems on this photo please help! i’m desperate for help!

Answer 1

`x=85\\ \\y=100\\ \\z=100`

Explanation:

Angles with measures of
`95^(\circ)` and
`x^(\circ)` are supplementary angles, thus, they add up to
`180^(\circ):`

`x+95=180\\ \\x=180-95\\ \\x=85`

Angles with measures of
`80^(\circ)` and
`y^(\circ)` are supplementary angles, thus, they add up to
`180^(\circ):`

`y+80=180\\ \\y=180-80\\ \\y=100`

Find the measures of two remaining interior angles of the pentagon:

`1. \ 180^(\circ)-62^(\circ)=118^(\circ)\\ \\2.\ 180^(\circ)-53^(\circ)=127^(\circ)`

The sum of the measures of all interior angles in the pentagon is

`(5-2)\cdot 180^(\circ)=540^(\circ),`

then

`95^(\circ)+118^(\circ)+100^(\circ)+z^(\circ)+127^(\circ)=540^(\circ)\\ \\440^(\circ)+z^(\circ)=540^(\circ)\\ \\z^(\circ)=100^(\circ)`