1. In the diagram below, line AB is parallel to line CD, EF = FG, <BEF = 100+x and <AEG=x. Find the value of x.
2. In the diagram below, WY = 9, XZ=7, [AWX]=30, and [AYZ] = 20. Find [AXY].
+130511 1) < BEF = < GFE and < AEG = < FGE [ a transversal cutting two parallel lines makes alternate interior angles equal]
Since EF = FG then < FGE = < GEF [ when two sides of a triangle are equal, the angles opposite those sides are also equal]
But < AEG = < FGE....so ..... <GEF = < AEG as well
And we have that
< GFE + < FGE + < GEF = 180 and by substitution
[100 + x ] + x + x = 180
100 + 3x = 180 subtract 100 from each side
3x = 80
x = 80/3 = about 26.66°
+130511 2) This problem is impossible......If <AYZ = 20 then < AYW = 160 because they are supplementary angles
But < AWX = 30 = < AWY.......which implies that in Δ AWY.... angles AWY and AYW would sum to 30 + 160 = 190°.......but this sum is greater than 180° which is not possible
