1.6 Angle Pair Relationships. Adjacent Angles  Remember: Adjacent Angles share a vertex and a ray, but DO NOT share any interior points.

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Presentation transcript:

1.6 Angle Pair Relationships

Adjacent Angles  Remember: Adjacent Angles share a vertex and a ray, but DO NOT share any interior points.

Which angle pairs are adjacent? <1&<2 <2&<3 <3&<4 <4&<1 Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays. Vertical Angles are always congruent! <1&<3, <2&<4 Then what do we call <1&<3?

Linear Pair (of angles)  2 adjacent angles whose non-common sides are opposite rays. 1 2 Basically, it’s 2 adjacent angles that together make a straight line!

Example  Vertical angles? <1 & <4  Adjacent angles? <1&<2, <2&<3, <3&<4, <4&<5, <5&<1  Linear pair? <5&<4, <1&<5  Adjacent angles not a linear pair? <1&<2, <2&<3, <3&<

Important Facts  Vertical Angles are congruent. ALWAYS! THIS IS ONE ASSUMPTION YOU CAN ALWAYS MAKE!  The sum of the measures of the angles in a linear pair is 180 o. REMEMBER: THE TWO ANGLES IN A LINEAR PAIR ARE Adjacent ANGLES THAT MAKE A STRAIGHT LINE!

Example:  If m<5=130 o, find m<3 m<6 m< = 130 o =50 o

Example:  Find x and y and m<ABE m<ABD m<DBC m<EBC 3x+5 o y+20 o x+15 o 4y-15 o x=40 y=35 m<ABE=125 o m<ABD=55 o m<DBC=125 o m<EBC=55 o A B C D E m<CBE + m<EBA = 180° Linear Pair x x + 5 = 180 Substitute 4x + 20 = 180 CLT 4x = 160 Subtraction x = 40 Division m<CBD + m<ABD = 180 Linear Pair 4y y + 20 = 180 Substitute 5y + 5 = 180 CLT 5y = 175 Subtraction POE y = 35 Division POE

Complementary Angles  2 angles whose sum is 90 o.  The two angles DO NOT need to be adjacent! o A 55 o B <1 & <2 are complementary <A & <B are complementary

Supplementary Angles  2 angles whose sum is 180 o.  Two angles can be supplementary and NOT BE A LINEAR PAIR o 50 o X Y <1 & <2 are supplementary. <X & <Y are supplementary.

Ex: <A & <B are supplementary. m<A is 5 times m<B. Find m<A & m<B.  Let’s say m<A = 5b m<B = b

Angle A’s measure is 3 times its complement, <B. The measure of angle A’s supplement, <C, is 5 times m<B. Find the measures of all the angles.  m<A + m<B = 90° 3b + b = 90  4b = 90 b = 22.5  m<A = 3*22.5= 67.5°  m<C = 5b, so 5(22.5) = 112.5°  Let’s say:  m<B = b  m<A = 3b  m<C = 5b