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Splash Screen. You will be able to Write proofs involving relationships of angles. Then/Now. Concept. Concept. Use the Angle Addition Postulate.

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Then now

Then/Now




Example 1

Use the Angle Addition Postulate

CONSTRUCTIONUsing a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?

Example 1


Example 11

Find m1 if m2 = 58 and mJKL = 162.

A. 32

B. 94

C. 104

D. 116

Example 1



Example 2

Use Supplement or Complement

TIMEAt 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?

Example 2


Example 21

QUILTINGThe diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.

A. 20

B. 30

C. 40

D. 50

Example 2






Example 3

Given:

Prove:

Proofs Using Congruent Comp. or Suppl. Theorems

Example 3


Example 31

Proof:

Statements Reasons

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Proofs Using Congruent Comp. or Suppl. Theorems

Example 3


Example 32

In the figure, NYR andRYA form a linear pair,AXY and AXZ form a linear pair, and RYA andAXZ are congruent. Prove that NYR and AXY are congruent.

Example 3


Example 33

Statements Reasons

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Example 3



Example 4

Proof:

Statements Reasons

Use Vertical Angles

If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.

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Example 4


Example 41

Use Vertical Angles

Statements Reasons

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Example 4