Chapter 9 - XYZ Custom Plus

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Chapter 9 Solving Equations and Inequalities
facts from geometry Angles
An angle is formed by two rays with the same endpoint. The common endpoint
is called the vertex of the angle, and the rays are called the sides of the
angle.
In Figure 1, angle θ (theta) is formed by the two rays OA and OB. The vertex
of θ is O. Angle θ is also denoted as angle AOB, where the letter associated
with the vertex is always the middle letter in the three letters used to denote
the angle.
Degree Measure The angle formed by rotating a ray through one complete
revolution about its endpoint (Figure 2) has a measure of 360 degrees,
which we write as 360°.
B
O
A
Figure 1
One complete revolution = 360
Figure 2
One degree of angle measure, written 1°, is } 1
360 } of a complete rotation of a
ray about its endpoint; there are 360° in one full rotation. (The number 360
was decided upon by early civilizations because it was believed that the Earth
was at the center of the universe and the Sun would rotate once around the
Earth every 360 days.) Similarly, 180° is half of a complete rotation, and 90°
is a quarter of a full rotation. Angles that measure 90° are called right angles,
and angles that mea sure 180° are called straight angles. If an angle measures
between 0° and 90° it is called an acute angle, and an angle that measures between
90° and 180° is an obtuse angle. Figure 3 illustrates further.
90
180
Right angle
Straight angle
Acute angle
Obtuse angle
D
Figure 3
Complementary Angles and Supplementary Angles If two angles
add up to 90°, we call them complementary angles, and each is called the
complement of the other. If two angles have a sum of 180°, we call them
supplementary angles, and each is called the supplement of the other. Figure
4 illustrates the relationship between angles that are complementary and
angles that are supplementary.
Complementary angles: 90°
Supplementary angles: 180°
Figure 4