Basic Mathematics for College Students

In Problems 35–38, first find. Then determine the measure of

each angle that is labeled in the figure.

35.

36.

37.

38.

APPLICATIONS

39. CONSTRUCTING PYRAMIDS The Egyptians
    used a device called a plummetto tell whether stones
    were properly leveled. A plummet (shown below) is
    made up of an A-frame and a plumb bob suspended
    from the peak of the frame. How could a builder use a
    plummet to tell that the two stones on the left are not
    level and that the three stones on the right are level?

Plummet

Plumb bob

7 x – 2°

2 x + 33°

AB

C D

ACBD

A

C

6 x – 2°

9 x – 38°

E

D

B

ABDE

5 x – 40°

3 x + 4°

C

DE

AB

ABDE

l 1

x

C A

B

3 x + 20°

l 1 CA

x 40. DIAGRAMMING SENTENCES English

instructors have their students diagram sentences to

help teach proper sentence structure. A diagram of

the sentence The cave was rather dark and dampis

shown below. Point out pairs of parallel and

perpendicular lines used in the diagram.

41. BEAUTY TIPS The figure to
    the right shows how one website
    illustrated the “geometry” of the
    ideal eyebrow. If and
    , find
    .


42. PAINTING SIGNS For many sign painters, the most
    difficult letter to paint is a capital E because of all the
    right angles involved. How many right angles are
    there?


43. HANGING WALLPAPER Explain why the
    concepts of perpendicularand parallelare both
    important when hanging wallpaper.


44. TOOLS What geometric concepts are seen
    in the design of the rake shown here?


45. SEISMOLOGY The figure shows how an
    earthquake fault occurs when two blocks of earth
    move apart and one part drops down. Determine
    the measures of , , and.

105°

1

2

3

 1  2  3

E

m(ABE)

m(DCF)130°

l 1 l 2

cave

dark

The anddamp

was

rather

734 Chapter 9 An Introduction to Geometry

F

C

B

E A

D

l 2

l 1