Course: Applied Geo. Aim: Complement your Supplement Aim: How to Complement your Supplement -...

Course: Applied Geo.Aim: Complement your Supplement

Aim: How to Complement your Supplement - Angle-wise

Do Now:

Write the definition of a linear pairon the slip of paper. Write the definition of adjacent angles.Hand the paper in with your name on it.


If the sum of the measures of two angles is 90 degrees, the angles are

called complementary angles.

Adjacent angles Non-adjacent angles

Complementary angles may be adjacent or non-adjacent.


Sketch Pad – Complementary s

Directions:1) Draw a right angle using the Ray Tool. 2) Make the bottom ray horizontal and the

up ray by holding the Shift key. 3) Label all points with the Text Tool. 4) Measure the angle with the Measure

Menu5) Draw a 3rd ray from vertex B between

the rays of the right angle.

It should look similar to this

6) Measure and Label the adjacent angles formed by this new ray.

7) What must be the sum of the two angles if they are complementary?

mABC = 90.0B A

CD


12

Find m 2, if m 1 = 73.50

A

B C

ABC is a right angle

Since ABC is a right angle (900), the sum of 1 + 2 = 900. If 73.50 + 2 = 900 ,

then 2 = 16.50

73.50

16.50

12

Find m 2, if m 1 = 48.20

A

B C


Since ABC is a right angle (900), the sum of 1 + 2 = 900. If 48.20 + 2 = 900 ,

then 2 = 41.8

73.50

16.50


A

B C


D

yFind m y, if m x = 81.30

A

B C


Since ABC is a right angle (900), the sum of x + y = 900. If 81.30 + y = 900 ,

then y = 8.70

If m ABD = 3x + 5 and m CBD = 280, find the value of x.

3x + 5

280

3x + 5 + 28 = 903x + 33 = 90

3x = 57 x = 19

x

3(19) + 5 = 62

62 + 28 = 90


Two angles are complementary. One angle measures x degrees and the other measures 2x degrees. What is the value of x and how many degrees in each of the angles?

Two angles are complementary. The larger angle of the two is 14 degrees bigger than the smaller angle. How many degrees in each angle?

The measure of the complement of an angle is 12o more than twice the measure of the angle. Find the measure of the angle and its complement.


If the sum of the measures of two angles is 180 degrees, the angles are called

supplementary angles.

Supplementary angles may be adjacent or non-adjacent

The angles show above are called a linear pair - adjacent

angles that are supplementary.


Sketch Pad – Supplementary s

Directions:1) Draw, label and measure a horizontal

Straight angle with the Ray Tool. (use Shift Key)

2) Draw and label a ray from the vertex

It should look similar to this

3) Measure each angle of the linear pair 4) What must be the sum of the two angles

if they are supplementary?

mABC = 180.0B AC

D


1 2

ABC is a straight angle

A B C

Find m 2, if m 1 = 53.70

1 + 2 = 1800

If 53.70 + 2 = 1800

then 2 = 126.30

53.70 126.30

x y


A B C

Find m y, if m x = 18.750

x + y = 1800

If 18.750 + y = 1800

then y = 161.250

18.750161.25


A B C

D

and m CBD = x + 20 find the value of x and the m CBD.


80 x + 20

If m ABD = 80

x + 20 + 80 = 180x + 100 = 180

x = 80

m CBD = x + 20

A B C

D

and m CBD = 4x + 2, find the value of x and each angle.


2x – 8 4x + 2

If m ABD = 2x – 8

m ABD = 62 – 8 = 540

2x – 8 + 4x + 2 = 180

x = 31

m ABD = 2x – 8

m CBD = 4(31) + 2 = 1260

m CBD = 4x + 2

m CBD = 80 + 20

m CBD = 100

6x – 6 = 1806x = 186


A

B C

D

The larger of 2 complementary s is twice the size of the smaller. Find the measure of each .

Let x = the smaller angleThen 2x = the larger angle

x + 2x = 90 3x = 90 x = 30

300

600

The measure of the larger of 2 supplementary s is 150 more than

twice the smaller. Find each . Let a = smaller Let 2a + 15 = larger 2a + 15 + a = 180

3a + 15 = 180 3a = 165 a = 550

550

2(550) + 151100 + 15

1250

550 + 1250 = 1800

x2x

Course: Applied Geo. Aim: Complement your Supplement Aim: How to Complement your Supplement -...

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