Angles

ANGLES

An angle ( ) is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle).
PARTS OF AN ANGLE
Vertex: A
B Sides: AB and AC
exterior of the angle
interior of
the angle
A 1 C
HOW TO NAME AN ANGLE
- BAC - CA B - 1 - A
Angles are measured in degrees.
The measure of A is written as m A. m A = 45 o .

CLASSIFICATION OF ANGLES (according to measure)
x o
ACUTE x o x o
0 < x < 90 o RIGHT
x = 90 o
REFLEX
x o 180 o < x < 360 o x o
OBTUSE STRAIGHT
90 o < x < 180 o x = 180 o

PROTRACTOR POSTULATE
Let OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers from 0 o to 180 o in such a way that OA is paired with 0 o to and OB is paired with 180 o or the way around.
Angles with the same measure are congruent.

ANGLE ADDITION POSTULATE
If point B is in the interior of  AOC, then
m  AOB + m  BOC = m  AOC .
If  AOC is a straight angle, then
m  AOB + m  BOC = 180 o .

Angle Pairs
Two coplanar angles are adjacent if and only if they satisfy three conditions:
they have a common vertex,
they have common side, and
they have no common interior points.
 AOB and  BOC are adjacent.
 ABC and  DEF are not.

Two angles are complementary if and only if the sum of their measures is equal to 90 o . Each angle is the complement of the other.
Two angles are supplementary if and only if the sum of their measures is equal to 180 o . Each angle is the supplement of the other

Find the complement.

What is the complement of 60°?
30°

55°

67°

9°

13°

87°

45°

Find the supplement.

What is the supplement of 30°?
150°

68°

85°

133°

172°

26°

34°

(mixed)

31°

165°

63°

none

80°

What is the complement of the supplement of 146°?
56°

What is the complement of the complement of 10°?
10°

What is the supplement of the supplement of 113°?
113°

20°

none°

What is the supplement of the complement of 14°?
114°

What is the supplement of the complement of 88°?
178°

What is the complement of x°?
(90-x)°

What is the supplement of x°?
(180-x)°

If  BAC is 20° more than its complement, what is its measure?
55°

An angle measures twice the measure of its complement. What is the angle?
60°

Angle BUM is 30° less than twice its complement. Find its measurement.
50°

An angle and its complement have a ratio of 2:3. What are their measurements?
36°, 54°

The difference between the measures of angle and its complement is 36°. Find their measurements.
63°, 27°

Angle CAT and angle DOG are supplementary. If m  CAT is thrice the m  DOG, what are their measurements?
135°, 45°

Find the size of the angle whose supplement is equal to six times its complement.
72°

The supplement of an angle measures 40° more than twice its complement. What is the measurement of the angle?
40°

The difference between the measures of two supplementary angles is 50 0 . Find the measure of the larger angle.
115°

Find the measure of  R if:
it is 50° more than its complement.
it is 12° less than its complement.
it is thrice its complement.
it is half its complement.
it is 58° more than thrice its complement.
it is twice the measure of its supplement.
it is 44° less than its supplement.
its supplement is thrice its complement.
its complement and supplement add up to 120 ° .
its complement is 90° less than its supplement.

Angles

by Fidelfo Moral

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Angles

by Fidelfo Moral

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Angles Presentation Transcript

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