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.