2. consider the following diagram. (a) name a pair of complementary angles. (b) name two supplementary angle pairs. (c) solve for each of the unknowns. show your work.

bc  cd  

ab   bd

2x+40=90

2x=50

X=25

5y+2(25)+40=180

5y+90=180

5y=90

y=18

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The supplementary angles are defined as angles whose sum is 180 degrees.

The complementary angles are defined as angles whose sum is 90 degrees.

(a) Name a pair of complementary angles.

Angles BC and CD

(b) Name two supplementary angle pairs.

Angles AB and BD

(c) Solve for each of the unknowns.

We know that BD is 90 degrees.

CD is given as 40 degrees.

So, angle BC is =50 degrees

or x=25 degrees. We can also say that BC is equal to 50 degrees.

Angle AB is also a right angle or 90 degrees because it lies on a straight line AD(whose sum is 180) with an already right angle BD.

So, 5y=90 degrees.

So, y=18 degrees.

x/3-10=8

x/3=18

x=48

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