November 2009
Beginner
368 pages
8h 55m
English
Content preview from Head First 2D Geometry
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you are here 4 35
finding missing angles
The angles of a four-sided shape add up to 360º
Squares and rectangles have four equal angles, a
quarter turn each, and even the most uneven four-
sided shape still has four angles adding up to 360º.
82º
103º
115º
60º
60º
115º
103º
82º
The four corners
of this shape…
Let’s step the investigation up a gear! Find the mystery angles marked
on the crime scene diagram, a, b, c, d, e, f, and the all important angle,
g, which lets us work out the bounce angles.
Hint: it’s worth going in alphabetical order.
BULLET
PATH
MICKY
BENNY
FOOTPRINTS
BROKEN
GLASS
18º
CRIME SCENE SKETCH
CASE GEO180
(ANGLES AS MEASURED
BUT DRAWING NOT TO
SCALE)
72º
CHARLIE
FOOTPRINTS
28º
158º
TIRE
TRACKS
56º
aº
bº
cº
dº
eº
fº
gº
18º
…come together
to make this.
36 Chapter 1
sharpen solution
Let’s step the investigation up a gear! Find the mystery angles marked
on the crime scene diagram, a, b, c, d, e, f, and the all important angle,
g, which lets us work out the bounce angles.
a)
b)
c)
28º
aº
a and 28º are complementary.
a + 28º = 90º, so a = 62º
The room is a four-sided shape and the other three corners are right angles, so
b = 360º - (90º + 90º + 90º) = 90º
62º
158º
cº
c is part of a four-sided shape, with aº
and the corner angle bº we just found, so
c = 360º - (158º + 62º + 90º) = 50º
BULLET
PATH
MICKY
BENNY
FOOTPRINTS ...
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