Question

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

Answer 1

Answer:

$x=85\\ \\y=100\\ \\z=100$

Step-by-step 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

$95^{\circ}+118^{\circ}+100^{\circ}+z^{\circ}+127^{\circ}=540^{\circ}\\ \\440^{\circ}+z^{\circ}=540^{\circ}\\ \\z^{\circ}=100^{\circ}$