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
B Sides: AB and AC
exterior 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)
ACUTE x o x o
0 < x < 90 o RIGHT
x = 90 o
x o 180 o < x < 360 o x o
90 o < x < 180 o x = 180 o
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.
Try This Measure the angles (#s 1 & 2 of Exercise 4-2 C – pg 56)
Use a protractor to draw a 105 o angle .
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 .
pls. refer to the examples in page 55
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.
AOB and AOC 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
Two angles are called vertical angles if and if only they are two nonadjacent angles formed by two intersecting lines.
2 1 B A 50 O 40 O 3 4 155 O 25 O A B 1 2 3 4
1 and 3
2 and 4
pls. refer to the examples in page 58
VERTICAL ANGLE TEST
If two angles are vertical, then they are congruent.