Download LESSON 1-5 (Part 1) Notes: SPECIAL ANGLE PAIRS

LESSON 1-5 (Part 1) Notes:
SPECIAL ANGLE PAIRS
[COMPLEMENTARY AND SUPPLEMENTARY ANGLES]
* TYPES OF ANGLES:
1. Acute:
Acute angles have measures between 00 and 900 degrees
[00 < measure < 900]
2. Right: A right angle has measure equal to 900.
[measure = 900]
3. Obtuse: Obtuse angles have measures between 900 and 1800.
[900 < measure <1800]
* SPECIAL PAIRS OF ANGLES:
1. COMPLEMENTARY ANGLES: Pair of angles whose sum of measures equals 900.
Examples:
400 and 500 angles are complementary angles because 400 + 500 = 900
Examples:
A 400 angle is called the complement of the 500 angle.
Similarly, the 500 angle is the complement of the 400 angle.
Practice: List two pairs of complementary angles.
Practice: Find the complement of each given angle.
a) 350
b) 480
c) 150
d) 300
* What type of angles are complementary angles?
2. SUPPLEMENTARY ANGLES:
Pair of angles whose sum of measures equals 1800.
Examples:
600 and 1200 angles are supplementary angles because 600 + 1200 = 1800
Examples:
A 600 angles is called the supplement of the 1200 angle.
Similarly, the 1200 angle is the supplement of the 600 angle.
Practice: List two pairs of supplementary angles.
Practice: Find the supplement of each given angle.
a) 400
b) 1300
c) 200
d) 1100
* Can two supplementary angles both be obtuse angles? Why or why not?
* Can two supplementary angles both be acute angles?
Why or why not?
* Can two supplementary angles both be right angles?
Why or why not?
* If two angles are supplementary and one of the angles is acute, what type of angle is the
other angle?
* OTHER DEFINITIONS:
ANGLE BISECTOR:
A ray (or line or segment) that divides an angle into two congruent
angles (two angles with equal measure).
A
is an angle bisector
∠ABE
∠EBC so m∠ABE = m∠EBC
B
E
EXAMPLES/PRACTICE:
C
1. Refer to the diagram to answer each.
a) Name 2 acute angles.
b) Name 2 obtuse angles.
1
2
3
c) Name 2 adjacent angles.
4
d) Name 2 vertical angles.
e) Name a supplement of ∠3.
2. Refer to the diagram to answer each.
a) If m∠ABE = 40, find m∠EBC.
is an angle bisector.
A
B
E
b) If m∠ABC = 70, find m∠ABE.
C
3. ∠1 and ∠2 are complementary.
Find x, m∠1 and m∠2.
∠1 = 5x + 4
∠2 = 2x + 2
5.
4. ∠1 and ∠2 are supplementary.
Find x, m∠1 and m∠2.
∠1 = 12x + 4
∠2 = 9x + 8
bisects ∠AOC. Find the values of x, m∠AOB, m∠BOC and m∠AOC.
∠AOB = 3x + 9
∠BOC = 5x + 10
LESSON 1-5 (Part 2) Notes:
SPECIAL ANGLE PAIRS
[LINEAR PAIR AND VERTICAL ANGLES]
* LINEAR PAIR: A pair of adjacent angles whose noncommon sides are opposite rays (form a line).
∠ABE and ∠EBC form a linear pair.
E
A
* LINEAR PAIR POSTULATE:
From above diagram:
B
C
Angles that form a linear pair are supplementary.
m∠ABE + m∠EBC = 1800.
* VERTICAL ANGLES: Two non-adjacent angles formed by the intersection of two lines. Vertical
angles are "opposite" of each other and share a common vertex.
∠1 and ∠3;
∠2 and ∠4
1
2
3
4
* VERTICAL ANGLES THEOREM:
Above: ∠1
Vertical angles are congruent.
EXAMPLES/PRACTICE:
Find the measure of each numbered angle.
1)
2)
1
1400
2
1
2
3
3
350
4
Find the value of x.
3)
4)
1130
7x − 12
9x − 5
4x + 27
∠3; ∠2
∠4
Find x, m∠A and m∠B if ∠A and ∠B are:
5) vertical angles
∠A = 5x − 20
∠B = 2x + 40
6) linear pair
∠A = 3x + 40
∠B = 7x − 10
7) vertical angles
∠A = 4x − 9
∠B = 2x + 5
8) linear pair
∠A = 6x + 9
∠B = 2x + 11
Refer to the diagram below to find x, m∠A and m∠B.
9) ∠A = 7x − 8
∠B = 4x − 1
A
B