Question

HELPPP!!!! 10 PTS!!

Find the missing information

x = _____

y = _____

m angle (x + 12) = _____

Answer 1

Focus on the triangle. One angle measures 31+x, the bottom right measures 45 (it is supplementary to a 135 angle). The bottom left measures x+12 because it is opposite to the x+12 angle. The sum of interior angles of a triangle must be 180, so we have

`(31+x)+45+(x+12)=180 \iff 2x+88=180 \iff 2x=92 \iff x=46`

Angle y is supplementary with the x+12 angle, so we have

`y=180-(x+12)=180-x-12=180-46-12=122`

Finally, angle x+12 measures 46+12=58

Answer 2

x=46

y=122

m angle (x+12)=58°

Explanation:

31+x+45+12+x=180

2x+88=180

x=46

y=122

x+12=58°