Page 201 - Math Course 2 (Book 2)

Proving Angle Relationships

Supplementary Angles
By the Angle Addition Postulate, the sum of the
two angles is 120, so the angle between the sec- If ∠1 and ∠2 are complementary angle and
ond and hour hands is also 60º. m∠1 = 62, find m∠2.

They are both 60º by the
Answer definition of angle bisector and A. 28
the Angle Addition Postulate B. 31
C. 56
D. 62

Supplementary Angles
Answer
Example

If ∠1 and ∠2 form a linear pair and m∠2 = 166, find
m∠1.
MO. 12 - L8b
m∠1 + m∠2 = 180 Supplement Theorem
m∠1 + 166 = 180 m∠2 = 166 Congruent and Right Angles
m∠1 = 14 Subtraction Property

Answer 14
THEOREMS

12.5 Congruence of angles is reflexive,
Your Turn! symmetric and transitive.

Angle Addition Reflexive ∠1 ≅ ∠1
Property
QUILTING
The diagram below shows one square for a
particular quilt pattern. If m∠BAC = m∠DAE = 20, Symmetric If ∠1 ≅ ∠2, then ∠2 ≅ ∠1
and ∠BAE is a right angle, find m∠CAD. Property

A. 20 Transitive If ∠1 ≅ ∠2, and ∠2 ≅ ∠3, then
B. 30 Property ∠1 ≅ ∠3
C. 40
D. 50
12.6 Angles supplementary to the same angle
or to congruent angles are congruent.

Abbreviation ⦞ suppl. to same ∠ or ≅ ⦞ are ≅.

Example: If m∠1 + m∠2 = 180 and
m∠2 + m∠3 = 180, then
∠1 ≅ ∠3.

2
3
1

Answer

193