Chapter 2 Section 4 Special Pairs of Angles

Define: complementary angles • Two angles who’s measures have the sum of 90. •

Define: Supplementary angles • Two angles whose measures have the sum of 180. •

Application of the supplementary angle definition 1 2 If two adjacent angles form a

Expressions for complements and supplements o Given an angle with the measure of 50.

example A supplement of an angle is 6 times as large as the complement

example If angle A and angle B are complementary angles and angle A is

Define: Vertical angles • Two angles such that the sides of one angle are

According to the angle addition postulate vertical angles also give us some special adjacent

So the numbers show that if the given o angle is 35 then the

Vertical Angle Theorem • If two angles are vertical, then they are congruent. Given:

examples Class exercises P 51 B A o o 40 60 O F E

Practice work • P 52 we 1 -18 all, 20 -32 e

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Chapter 2 Section 4 Special Pairs of Angles

Define: complementary angles • Two angles who’s measures have the sum of 90. • Each angle is called a complement of the other 56 o 1 2 34 o

Define: Supplementary angles • Two angles whose measures have the sum of 180. • Each angle is called a supplement of the other. o 60 A o 120 B Angle A and angle B are supplementary angles

Application of the supplementary angle definition 1 2 If two adjacent angles form a straight angle then m<1 +m<2 = 180 by the angle addition postulate If m<1 + m<2 = 180 then <1 and <2 are supplementary by the definition of supplementary angles

Expressions for complements and supplements o Given an angle with the measure of 50. What is the measure of the complement and the supplement? o Comp= (90 - 50) = 40 o supp= (180 - 50) = 130 o Given an angle with the measure of x. What is the measure of the complement and the supplement? o o Comp= (90 -x) supp= (180 -x) o Given an angle with the measure of 2 n-45. What is the measure of the complement and the supplement? o Comp= [90 -(2 n-45)] = (135 -2 n) o o supp= [180 -(2 n-45)] = (225 -2 n) o

example A supplement of an angle is 6 times as large as the complement of the angle. Find the measure of the angle, its supplement, and its complement.

example If angle A and angle B are complementary angles and angle A is x+16 and angle B is 2 x-16, then find the measure of angle B.

Define: Vertical angles • Two angles such that the sides of one angle are opposite rays to the sides of the other angle. • Thus, when two lines intersect, they form two pairs of vertical angles. 2 <1 and <3 are vert. angles 1 4 3 <2 and <4 are vert. angles

According to the angle addition postulate vertical angles also give us some special adjacent angle pairs 2 If the two adjacent angles form a straight angle (picture) 1 4 3 Then m<2 + m<1 = 180 What are the other pairs of angles o that have a sum of 180 ? Angle addition postulate

So the numbers show that if the given o angle is 35 then the other angles are… o o 35 145 o 35 And we would see that: If the angles are vertical then congruent or equal they are__________. So prove it!!!

Vertical Angle Theorem • If two angles are vertical, then they are congruent. Given: Prove: 2 and 2@ 4 are vertical 4 2 1 4 3

examples Class exercises P 51 B A o o 40 60 O F E D C

Practice work • P 52 we 1 -18 all, 20 -32 e