19.1 Angles formed by intersecting lines.ppt

• Identify Angle Pair Relationships formed by a
line.
• Adjacent Angles
• Vertical Angles
• Linear Pair
• Complementary Angles
• Supplementary Angles

(def) An ACUTE ANGLE is an angle with a MEASURE less
than 90°.
(def) A RIGHT ANGLE is an angle with a MEASURE = 90°
(def) An OBTUSE ANGLE is an angle with a MEASURE
greater than 90° but less than 180 °.
(def) A STRAIGHT ANGLE is an angle with a MEASURE =
180°.
Interior of angle
Exterior of angle
Do not COPY!!

Draw a Acute Angle and write the definition:

Draw a Obtuse and Right Angle,
and write the definition:

To Name an Angle - either use 3 letters or number it,
never use only 1 letter unless there is only one angle
with that vertex. If you use three letters, the vertex
must be the middle letter.
A
or never use
in this type of problem since more than
one angle has a vertex of B.
ABD
 1
 B

B
D
E
1

(def) ADJACENT ANGLES are 2 coplanar angles that share
a common ray and vertex but no common interior pts.
(def) An ANGLE BISECTOR is a ray that divides
an angle into 2 congruent angles.
ABD DBC
  
A
B
D
C

ANGLE ADDITION POSTULATE - If D is in the interior
of , then
i.e. The sum of the parts = whole
m ABD m DBC m ABC
    
ABC

A
D
C
B

(def) SUPPLEMENTARY ANGLES are 2 angles
whose measures have a sum of 180°.
or
145° 35°

(def) COMPLEMENTARY ANGLES are 2 angles
whose measures have a sum of 90°.
or
50° 40°

What is supplementary and complementary angles,
Give example and definition:

(def) LINEAR PAIR ANGLES are 2 adjacent angles
whose non-common sides form a line.
Linear Pair Theorem - If 2 angles form a linear
pair, then they are supplementary.

(def) VERTICAL ANGLES are 2 nonadjacent angles
formed by intersecting lines
Vertical Angles Theorem - If 2 angles are vertical
angles, then they are congruent.

What is Vertical Angles Theorem and
Linear Pair Theorem, Give example and definition.

SOLUTION
EXAMPLE 1
To find vertical angles, look or angles formed
by intersecting lines.
To find linear pairs, look for adjacent angles whose noncommon
sides are opposite rays.
Identify all of the linear pairs and all of the vertical angles in
the figure at the right.
1 and 5 are vertical angles.
ANSWER
1 and 4 are a linear pair. 4 and 5
are also a linear pair.
ANSWER

SOLUTION
EXAMPLE 2
Let x° be the measure of one angle. The
measure of the other angle is 5x°. Then
use the fact that the angles of a linear
pair are supplementary to write an
equation.
Two angles form a linear pair. The measure of one angle is 5
times the measure of the other. Find the measure of each angle.
ALGEBRA
x + 5x = 180°
6x = 180°
x = 30°
The measures of the angles are 30°
and 5(30)° = 150°.
ANSWER

The measure of an angle is twice the measure of
its complement. Find the measure of each angle.
Let x° be the measure of one angle . The measure of
the other angle is 2x° then use the fact that the angles
and their complement are complementary to write an
equation
x° + 2x° = 90°
3x = 90
x = 30
Write an equation
Combine like terms
Divide each side by 3
ANSWER The measure of the angles are 30° and
2( 30 )° = 60°
You Do
SOLUTION

To find the complement of an angle that
measures x°, do by subtracting its measure
from 90°, or (90 – x)°.
To find the supplement of an angle that
measures x°, do by subtracting its measure
from 180°, or (180 – x)°.

Find the measure of each of the following.
A. complement of F
B. supplement of G
90 – 59 = 31
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
(90 – x)

Find the measure of each of the following.
A. complement of F
B. supplement of G
90 – 41 = 49
(180 – x)
180 – (4x-5) = 180 – 4x + 5
= (185 – 4x)
(90 – x)
41
(4x-5)

An angle is 10° more than 3 times the measure of its
complement. Find the measure of the complement.
x = 3(90 – x) + 10
x = 270 – 3x + 10
x = 280 – 3x
4x = 280
x = 70
The measure of the complement, B, is (90 – 70) = 20.
Substitute x for mA and 90 – x for mB.
Distrib. Prop.
Divide both sides by 4.
Combine like terms.
Simplify.
Step 1 Let mA = x°. Then B, its complement
measures (90 – x)°.
Step 2 Write and solve an equation.

An angle is 15° more than 5 times the measure of its
complement. Find the measure of the complement.
x = 5(90 – x) + 15
x = 450 – 5x + 15
x = 465 – 5x
6x = 465
x = 77.5
The measure of the complement, B, is (90 – 77.5) = 12.5.
Substitute x for mA and 90 – x for mB.
Distrib. Prop.
Divide both sides by 4.
Combine like terms.
Simplify.
Step 1 Let mA = x°. Then B, its complement
measures (90 – x)°.
Step 2 Write and solve an equation.

4x +8
6x - 42
Solve for x and find each angle measurement.

19.1 Angles formed by intersecting lines.ppt

3x - 5
6x + 34

4x - 10
(2x – 7)

Find a Missing Angle Measure
The two angles below are supplementary. Find the
value of x.
155 + x = 180 Write an equation.
Answer: 25
Subtract 155 from each side.
Simplify.
=

1. A
2. B
3. C
4. D
A B C D
0% 0%
0%
0%
x = 35º
The two angles below are complementary. Find the
value of x.

Find a Missing Angle Measure
Use the two vertical angles
to solve for x.
Answer: 22º
68 + x = 90 Write an equation.
Find the value of x in the figure.
– 68 =– 68 Subtract 68 from each side.
x = 22 Simplify.

1. A
2. B
3. C
4. D
A
B
C
D
0% 0%
0%
0%
Find the value of x in the figure. X = 20º

Two adjacent angles (common vertex and
a common ray) that form a straight line. So
the two angles add up to ?
180º

Directions:
Identify each pair of angles as
vertical,
supplementary,
complementary,
linear pair
or none of the above.

#1
60º
120º
Supplementary
Angles
And a Linear Pair

#2
60º
30º
Complementary
Angles

#4
60º
40º
None of the above

#6
45º
135º
Supplementary Angles
and a Linear Pair

#7
65º
25º
Complementary Angles

#8
50º
90º
None of the above

Directions:
Determine the missing
angle.

19.1 Angles formed by intersecting lines.ppt

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19.1 Angles formed by intersecting lines.ppt