welcome back 1. please pick up your skill builder and weekly homework. 2. turn in your extra credit...
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WELCOME BACK1. Please pick up your SKILL BUILDER and
WEEKLY HOMEWORK.2. Turn in your EXTRA CREDIT along with
your Builder 28 to the tray.3. COPY DOWN THE AGENDA for the
WEEK. TEST FRIDAY!!!3. Please complete the first 2 sections of
your SKILL BUILDER now.
-7c + 5 -6f + 5 18c + 24 -8g - 6
x -22 1
𝑥22x 20
Identify each pair of angles as complementary, supplementary,
or neither.
1. 2. 3.
4. Write and solve an equation to determine the value of x.
5. Tell whether the following statement is true or false. Angles are
complementary if the sum of their measures is 180°.
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o.
32
1
m<1 + m<2 + m<3 = 180°
The sum of all the angles equals 180º degrees.
90º 30º
60º
60º90º30º+
180º
Property of triangles
90º 50º
40º
40º90º50º+
180º
The sum of all the angles equals 180º degrees.
Property of triangles
60º60º60º+
180º60º 60º
60º
The sum of all the angles equals 180º degrees.
Property of triangles
Ex: 1What is the missing angle?
70º70ºx+
180º70º 70º
x
180 – 140 = 40˚
90º30ºx+
180º30º 90º
x
180 – 120 = 60˚
EX: 2 What is the missing angle?
60º60ºx+
180º60º 60º
x
180 – 120 = 60˚
Ex: 3What is the missing angle?
30º78º
X+
180º78º 30º
X
180 – 108 = 72˚
EX 4:What is the missing angle?
40º40º
?+
180º40º 40º
?
180 – 80 = 100˚
What is the missing angle?
45x 10x
35x
90°, 70°, 20°
Find all the angle measures
180 = 35x + 45x + 10x
180 = 90x
2 = x
What can we find out?
The ladder is leaning on the ground at a 65º angle. At what angle is the top of the ladder touching the building?
180 = 65 + 90 + x
180 = 155 + x25˚ = x
Extention to Triangle Sum Theorem
The acute angles of a right triangle are complementary.
m A + m B = 90∠ ∠ o
The tiled staircase shown below forms a right triangle.
The measure of one acute angle in the triangle is twice the measure of the other angle.
Find the measure of each acute angle.
Find the missing angles.
Con’t
Find the missing angles.
2x + x = 90
3x = 90
x = 30˚
2x = 60˚
SOLUTION:
Find the missing angles.
2x + (x – 6) = 90˚
3x – 6 = 90
3x = 96
x = 32
2x = 2(32) = 64˚
(x – 6) = 32 – 6 = 26˚
Example: Find x and the measure of each angle.
C
(𝟗 𝒙−𝟒)𝟎x =
m<A=
m<B=
m<C=
A
B
(𝟖𝟔)𝟎
(𝟕 𝒙+𝟐)𝟎
Example: Find x and the measure of each angle.
C
(𝟏𝟏𝒙−𝟕)𝟎x =
m<A=
m<B=
m<C=
A
B
(𝟕𝟓)𝟎
(𝟒 𝒙+𝟕)𝟎
Example: Find x and the measure of each angle.
C
(𝟓 𝒙)𝟎x =
m<A=
m<B=
m<C=
A
B
(𝟒 𝒙 )𝟎
Example: Refer to the diagram below to complete the table.
𝟑𝟎𝟎
2
3𝑨 1 4
𝑩
𝑪
𝒎<𝟏𝒎<𝟐𝒎<𝟏+𝟐𝒎<𝟑𝒎<𝟒
𝟑𝟎𝟎
𝟒𝟎𝟎
𝟒𝟎𝟎
𝟕𝟎𝟎
𝟖𝟎𝟎
𝟖𝟎𝟎
𝟗𝟎𝟎
Find the value of x.
The measures of three angles of a triangle are given by (8x 5)°, (2x)°, and (3x 10)°. What is the measure of the largest angle?
TRIANGLE SUM THEOREM
This packet is due Thursday. Please complete # 1-16 tonight for homework as well as your
Weekly Homework.