In the figure below, m WXY=71° and M1=37°. Find M2

∠ 2 = 34°

Step-by-step explanation:

∠ 1 + ∠ 2 = ∠ WXY , that is

37° + ∠ 2 = 71° ( subtract 37° from both sides )

∠ 2 = 34°

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct