Download 17 Angle1

Math with Measurements – Angle I
Angles are seen in many figures. To a mathematician, an angle is a figure formed by two rays
with the same endpoint. The endpoint is called the vertex of the angle.
This angle is named as ∠ B (angle B) or ∠ ABC (with the vertex
named in the middle).
Angles are measured in degrees. The symbol for degrees is a little
circle °.
Angle Facts:



The FULL CIRCLE is 360° (360 degrees).
A half circle or a straight angle is 180°.
A fourth of a circle or a right angle is 90°.
A special instrument, called a protractor, is used to measure an angle. The instrument is half
a circle, marked with 180 divisions that are called degrees. To measure an angle, place the
center of the base of the protractor on the vertex of the angle and line up the base with one of
the sides of the angle. Then read the number where the other side of the angle intersects the
marked circle of the protractor. Below you see a picture of how to measure an angle with a
protractor.
Take care to read from the right set of numbers. A protractor has two sets of numbers: one
set goes from 0 to 180, the other set from 180 to 0. Which one you read depends on how you
place the protractor: place it so that one side of the angle lines up with one of the zeros, and
read that set of numbers.
In the examples above we lined up the one side of the angle with the zero of the lower set of
numbers, so we need to read the lower set of numbers.
Practice
1
1. Measure the angles.
35
72
18
50
Angles are classified according to their measures.
Acute Measures less than 90°
Right Measures 90°
Obtuse Measures greater than 90°, but less than 180°
Straight Measures 180°
Special Angles:
Two angles are complementary if the sum of their measures is 90°.
Two angles are supplementary if the sum of their measures is 180°.
These two angles (40° and 50°) are Complementary Angles, because they
add up to 90° (a right angle).
These two angles (140° and 40°) are Supplementary Angles, because
they add up to 180° (a straight angle).


"C" of Complementary stands for "Corner"
(a Right Angle), and
"S" of Supplementary stands for "Straight" (180 degrees is a straight line)
2
Additional angle facts
 The angles in a triangle add up to 180o
 A straight line is 180o
 Parallel lines have equal angles
The last fact may require a picture. Notice the parallel lines create two groups of angles that
are all the same. If two parallel lines are cut by a transversal, then each pair of
corresponding angles is congruent.
corresponding angles
=
=
Vertical Angles are the angles opposite each other when two lines cross. For example,
angles 2 and 3 is a pair of vertical angles.
Symbol for minutes: (') This is similar to the symbol for feet. Symbol for seconds: (") This is
similar to the symbol for inches. The number of degrees of arc in a circle is 360. The sum of
the measures in degrees of the internal angles of a triangle is 180.
Two lines that intersect to form right angles
are perpendicular. The symbol
means
is perpendicular to.
Two lines in the same plane that never
intersect are parallel. The symbol means
is parallel to.
3
2. In this figure, PQ and RS are parallel (PQ||RS).
Of the following, which pair of angles
has the sum of 180°?
a.
∠5 and ∠7
b.
∠3 and ∠6
c.
∠1 and ∠5
d.
∠1 and ∠7
e.
∠ 2 and ∠8
3. In the left figure above, x = 40 and y =
60, what is the value of z?
80
(180 – 40 – 60 = 80)
4. What is the measure of ∠ABD?
∠ABD = 180 – 145 = 35
5. What is the measure of the missing interior angle for the figure shown below?
N = 120
4
6.
What is the measure of ∠QON?
∠QON = 90 – 64 = 26
7. AB and CD are straight lines. Find the unknown angles.
∠AOC = 152
∠DOB = 152
∠COB = 28
8. If the measure of ∠3 is 80°, which of the following is NOT true?
A. ∠4 measures 100°
B. ∠7 measures 80°
C. ∠5 measures 100°
D. ∠1 measures 80°
5