Algebra + Geometry Challenge 144

Geometry Level 2

It is given that $AB || CD$ and $XY || WZ$ ,

Red Angle = $90°$ , Green Angle = $130°$ ,

Blue Angle = $x^{2}$ , Brown Angle = $x^{2} - x + √80° + 40°$ ,

Then find the measure of Blue Angle + Brown Angle(in degrees).

Note: $x$ is in degrees.

1 solution

X X
May 3, 2018

$\angle YXD=40$ , $\angle YXZ=\angle YXD+\angle DXZ=40+x^2$ , $\angle YXZ=\angle XZW$ ,

so $x^2+40=x^2-x+\sqrt{80}+40$ , $x=\sqrt{80}$ ,the 2 angle sum $=80+120=200$ (in degrees)