7-66th grade math

Angle Pairs

Objective

• To find the measure of an unknown angle from its relationship to other angles

• Why? To know how to ‘read’ angle pairs will help you get a good foundation for geometry, later in high school math.

California State Standards MG 2.2 : Use the properties of complementary

and supplementary angles … to solve problems involving an unknown angle.

MG 2.1: Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these forms.

AF 1.1 : Write and solve one-step linear equations in one variable.

AF 3.2: Express in symbolic form simple relationships arising from geometry.

Vocabulary• Vertical angles– Two angles formed by intersecting lines and having no sides

in common. They have the same angle ∠ m. ̮͡�

• Supplementary angles– Two angles whose sum of their measures equals 180°

• Complementary angles– Two angles whose sum of their measures equals 90°

• Adjacent angles– Two angles that have a common vertex and a common side

but do not overlap.

Vocabulary • Intersecting angles or lines– Two lines or angles that have exactly one point in

common

• Perpendicular lines– Two lines that intersect and form a 90° angle ┐

• Parallel lines– Two lines that will never intersect each other

How to Find Measures of Angles w/o a Protractor

1) Observe and/or trace the angles needed to be identified: adjacent?, supplementary?, complementary?, vertical?

2) If vertical, the angles are the same. If adjacent, are angles supplementary or complementary? If supplementary, subtract from 180°. If complementary, subtract from 90 °.

3) Check your work.

F 147° H

E G J

∠GEJ and FEH are vertical angles∠∠GEJ = 147 °, so FEH = 147∠ °

If GEH = 180°, GEJ = 147∠ ∠ °, so HEJ = 180 - 147 = 33. HEJ = 33°∠ ∠

Then HEJ = 33°, so ∠ ∠GEF = 33°

How to Find Measures of Angles w/o a Protractor

C 50°

A O D∠AOC and ∠COD are

adjacent, supplementary angles, and m∠COD = 50°. Find ∠AOC.

180 – 50 = 130∠AOC = 130°

N M 25°

L K

∠KLM and ∠MLN are adjacent, complementary angles and m∠MLN = 25°. Find ∠KLM.

90 – 25 = 65∠KLM = 65 °

Try It!Find the m.∠1) a

35°

2) 79°

b

3) 110° c

4) d 50°

130°

1) 55, complementary

2) 79, vertical

3) 70, supplementary

4) 80, supplementary

5) Draw: m∠ of 120° with an adjacent supplementary angle, name this angle.

6) Draw: m∠ of 45° with an adjacent, name this angle.

7) Two angles that are congruent and supplementary. What are their m∠ ?

5) 60° 120°

6) 45°

45°

7) 90° and 90°

Objective Review • To find the measure of an

unknown angle from its relationship to other angles

• Why? You now know how to ‘read’ angle pairs will help you get a good foundation for geometry, later in high school math.

• Knowing the relationships of certain pairs of angles can help you find the measure of an unknown angle.

Independent Practice

• Complete problems 8-19

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 20-22

• If still more time, work on Accelerated Math.