1.5 Angle Relationships

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1.5 Angle Relationships. Objective: Identify special pairs of angles and perpendicular lines. CLE 3108.3.1 Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons. Measure. mA = 90 mB &lt; 90 mC &gt; 90.

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### 1.5 Angle Relationships

Objective: Identify special pairs of angles and perpendicular lines.

CLE 3108.3.1 Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons.

Measure
• mA = 90
• mB < 90
• mC > 90

A

B

C

Angle Practice
• Draw an angle of 60; Label as A
• Copy angle using compass. Label as B
• Bisect angle using compass.
• Measure angle of the two bisected sections using protractor.
• Label size of two new angles on drawing
Pairs of Angles

A

• Vertical Angles
• Linear Pair
• Same vertex & common side
• Two non-adjacent angles formed by two intersecting lines
• Adjacent angles whose non-common sides are opposite rays

C

D

B

B

A

E

AEB and DEC

AED and BEC

C

D

DEB and BEC

Are a linear pair

B

C

D

E

Identify the angles
• Two Obtuse Vertical Angles
• AEB, DEC
• AED, BEC
• Name two angles that form a linear pair
• AEB, DEC

A

B

E

D

C

Pairs of Angles
• Complementary Angles
• Supplementary Angles
• Two angles whose measure have a sum of 90
• Two angles whose measures have a sum of 180 

2

1 and 2 are complementary

1

3

4

3 and 4 are supplementary

Pairs of Angles

B

• Perpendicular Lines
• Intersect to form 4 right angles
• AB

A

Calculate Angle
• 1 + 2 = 90
• 1 = 90 - 2
• 1 - 2 = 12
• 1 = 12 + 2
• 12 + 2 = 90 - 2
• 12 + 2 x = 90 - 2 x
• 2x = 78
• x = 39
• 2 = 39
• 1 = 90 - 2 39
• 1 = 51
• Find the measure of two complementary angles if the difference in the two angles is 12.

1

2

To be perpendicular

2x + 5x + 6 = 90

7x = 84

x = 12

4y-2 = 90

4y = 92

y = 23

Find the value of X

Vertical Angles are congruent

2x + 25 = 3x – 10

35 = x

Linear Pair are supplementary

2x + 25 + y = 180

2(35) + 25 + y = 180

70 + 25 + y = 180

Y = 95

Assignment
• Block Class
• Page 51, 8 - 40 every 4th
• Honors Class
• Page 51, 20 - 44 every 4th, 50, 54,56