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Aim: How to Complement your Supplement - Angle-wise. Do Now:. Write the definition of a linear pair on the slip of paper. Write the definition of adjacent angles. Hand the paper in with your name on it. Complementary Angles.

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slide1

Aim: How to Complement your Supplement - Angle-wise

Do Now:

Write the definition of a linear pair

on the slip of paper.

Write the definition of adjacent angles.

Hand the paper in with your name on it.

slide2

Complementary Angles

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

Complementary angles may be adjacent or non-adjacent.

Adjacent angles Non-adjacent angles

slide3

Sketch Pad – Complementary s

  • Directions:
  • Draw a right angle using the Ray Tool.
  • Make the bottom ray horizontal and the up ray by holding the Shift key.
  • Label all points with the Text Tool.
  • Measure the angle with the Measure Menu
  • Draw a 3rd ray from vertex B between the rays of the right angle.

It should look similar to this

  • Measure and Label the adjacent angles formed by this new ray.
  • What must be the sum of the two angles if they are complementary?
slide4

ABC is a right angle

A

Find m2, if m 1 = 73.50

73.50

1

16.50

2

B

C

Since ABC is a right angle (900), the sum of 1 +2 = 900. If 73.50+2 = 900 , then2 = 16.50

ABC is a right angle

A

Find m2, if m 1 = 48.20

73.50

1

16.50

2

B

C

Since ABC is a right angle (900), the sum of 1 +2 = 900. If 48.20+2 = 900 , then2 = 41.8

slide5

A

ABC is a right angle

If m ABD = 3x + 5

D

and m CBD = 280, find the value of x.

B

C

ABC is a right angle

A

y

Find my, if m x = 81.30

x

B

C

Since ABC is a right angle (900), the sum of x+y= 900. If 81.30+y= 900 , theny= 8.70

3x + 5

280

3x + 5 + 28 = 90

3x + 33 = 90

3(19) + 5 = 62

3x = 57

62 + 28 = 90

x = 19

slide6

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.

slide7

Supplementary Angles

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.

slide8

Sketch Pad – Supplementary s

  • Directions:
  • 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?

slide9

ABC is a straight angle

Find m2, if m 1 = 53.70

53.70

126.30

1

2

1 +2 = 1800

A

B

C

If 53.70+2 = 1800

then2 = 126.30

ABC is a straight angle

Find my, if m x = 18.750

161.25

18.750

x

y

x+y= 1800

A

B

C

If 18.750+y= 1800

theny= 161.250

slide10

ABC is a straight angle

D

If m ABD = 80

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

the m CBD.

80

x + 20

A

B

C

x + 20 + 80 = 180

m CBD = x + 20

x + 100 = 180

m CBD = 80 + 20

x = 80

m CBD = 100

ABC is a straight angle

D

If m ABD = 2x – 8

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

2x – 8

4x + 2

A

B

C

2x – 8 + 4x + 2 = 180

m ABD = 2x – 8

6x – 6 = 180

m ABD = 62 – 8= 540

6x = 186

m CBD = 4x + 2

x = 31

m CBD = 4(31) + 2 = 1260

slide11

The measure of the larger of 2 supplementary s is 150 more than twice the smaller. Find each .

550

2(550) + 15

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

A

D

2x

x

B

C

Let x = the smaller angle

300

Then 2x = the larger angle

600

x + 2x = 90

3x = 90

x = 30

Let a = smaller 

Let 2a + 15 = larger 

1100 + 15

2a + 15 + a = 180

1250

3a + 15 = 180

3a = 165

550 + 1250 = 1800

a = 550