Download Angle Addition Postulate

Angle Classification
Acute angles measure more than 0 degrees
but less than 90 degrees.
Right angles measure exactly 90 degrees.
Perpendicular lines form right angles.
Obtuse angles measure greater than 90
degrees but less than 180 degrees.
A straight angle (line) has a measure of 180
degrees.
Angle Addition Postulate
If D is in the interior of ABC , then mABD  mDBC  mABC .
Angle Relationships
Adjacent angles – Coplanar angles that
have a common vertex and one common
side, but no common interior points
BAC and CAD
B
A
D
Vertical angles – Two non-adjacent angles
formed by two intersecting lines
1 & 2, 3 & 4
1
Linear pair – Two adjacent angles whose
non-common sides are two rays going in
opposite direction
1 & 2
Complementary angles – Sum of the
measures of the two angles is 90 degrees.
Supplementary angles – Sum of the
measures of the two angles is 180 degrees.
If two angles form a linear pair, they are
supplementary.
C
1
3
4
2
2
30o
60o
120o
60o
Angle Theorems
 Vertical angles are congruent.
 If two angles are supplementary to the same angle or to congruent angles, they are
congruent.
 If two angles are complementary to the same angle or to congruent angles, they are
congruent.
Examples
Use the figure to answer problems
#1 - 2 below.
C
A
O
B
D
1. If m AOC = 16x – 20 and m BOD = 13x+7, find the value of x and the degree measure
of the two angles.
x = 9, m  AOC = m  BOD = 124 º
2. If m AOB = 4x + 15 and m AOC = 3x + 25, find the degree measures of AOB and
AOC .
x = 20, m  AOB = 95 º and m  AOC = 85 º
Solve the following problems using the given information.
3.
X and Y are complementary angles. If m X = 3x + 7 and m Y = 6x+20, find the
value of x and the degree measure of each angle.
x = 7, m  X = 28 º, m  Y = 62 º
4. The measure of the complement of an angle is one-fourth the measure of the
supplement of the angle. Find the measure of the angle.
The angle measures 60 º.
x = angle
90 – x = complement
180 – x = supplement
complement = (1/4)supplement
90 – x = (1/4)(180 – x)
360 – 4x = 180 – x
180 = 3x
x = 60