finding missing angles

Angles can be made up of other, smaller angles

If you cut up an angle into pieces, the smaller angles

add up to the original angle.

+

=

BULLET

PA

TH

DOOR

MICKY

BENNY

FOOTPRINTS

BULLET FOUND

STUCK IN WALL HERE

18º

CRIME SCENE SKETCH

CASE GEO180

(ANGLES AS MEASURED

BUT DRAWING NOT TO

SCALE)

81º

86º

In the sketch,

this angle is made up

of these t

w

o, sma

ller

angles.

18º

PLAN VIEW

Angle Magnets

Which of these angles matches the mystery angle?

62º 72º 45º 67º

you are here 4 7

18º

?º

…and this marking

come t

ogether to make this angle…

18º + 72º = 90º

or you could jus

t tes

t a

ll the magnets y

ou were

giv

en t

o find one that fits—making 90º.

angle magnets solution

Angle Magnets Solution

Which of these angles matches the mystery angle?

18º

?º

62º 72º 45º

?º

18º + ?º = 90º

18º

67º

means i

t’s a

r

ight angle = 90º.

We know that these tw

o angles

18º

72º

Y

ou could hav

e done 90–18 t

o find the 72º,

Q:

I checked that mystery angle with a protractor and it

wasn’t 72º—so how come you’re saying it is?

A:In geometry, unless you’re specifically told to measure

an angle, assume that the drawing isn’t accurate, but that the

numbers on the sketch are. We calculate missing angles rather

than measure them.

Q:

What about all the other lines on the diagram? Do we

know if they’re straight?

A:The other line segments on the sketch represent things

like walls or the path between two points. They’re all definitely

straight. In fact, the two line segments we’re interested in—the

bullet path and the path from Benny to Micky—are also straight.

What we need to find out is whether they join up to form one

single straight line.

Chapter 1 8

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