Angle Pair Relationships Chapter 1 Section 1.6 Angle Pair Relationships

Warm-Up  

1 and 2 form a linear pair m1 + m2 =180° Two adjacent angles form a linear pair if their noncommon sides are opposite rays. Form a straight angle. Any two angles that form a linear pair have a sum of 180°.

Vertical Angles 1 2 3 4 1 and 3 are vertical angles 4 and 2 are vertical angles Two angles are vertical if their sides form two pairs of opposite rays. Vertical Angles are congruent

Use the figure to answer the questions Are 1 and 2 a linear pair? Yes Are 4 and 5 a linear pair? No Are 3 and 1 vertical angles? Are 2 and 5 vertical angles?

Use the figure to answer the questions If m6 = 51°, then m7 = _____ 129° -- Linear Pair If m8 = 103°, then m6 =_____ 103° -- Vertical Angles If m9 = 136°, then m8 =_____ 44° -- Linear Pair If m7 = 53°, then m9 =_____ 53° -- Vertical Angles

A and B are complementary Complementary Angles A 30° 60° B mA + mB = 90 ° A and B are complementary Two angles are complementary if their sum is 90°. Each Angle is the complement of the other

A and B are complementary Supplementary Angles A 120° 60° B mA + mB = 180 ° A and B are complementary Two angles are supplementary if their sum is 180°. Each angle is the supplement of the other

A and B are complementary and B and C are supplementary If mA = 48° then mB = _____ and mC = _____ mA + mB = 90° 48° + mB = 90° mB = 42° mB + mC = 180° 42° + mC = 180° mC = 138°

A and B are complementary and B and C are supplementary If mB = 83° then mA = _____ and mC = _____ mA + mB = 90° mA + 83° = 90° mA = 7° mB + mC = 180° 83° + mC = 180° mC = 97°

A and B are complementary and B and C are supplementary If mC = 127° then mB = _____ and mA = _____ mC + mB = 180° 127° + mB = 180° mB = 53° mA + mB = 90° mA + 53° = 90° mA = 37°

A and B are complementary and B and C are supplementary If mA = 25° then mB = _____ and mC = _____ mA + mB = 90° 25° + mB = 90° mB = 65° mB + mC = 180° 65° + mC = 180° mC = 115°

Find the value of the variable Vertical Angles are congruent Solve for x 2x + 40 = 110 2x = 70 x = 35° Solve for y y + 20° = 70° y = 50°

Find the value of the variable Linear Pairs are add up to 180° Vertical Angles are congruent x + 168° = 180° x = 12° y = 168°

Find the value of the variable Vertical Angles are congruent Solve for x 48 + x = 64 x = 16 Solve for y 8y + 36 = 14y – 24 36 = 6y – 24 60 = 6y 10 = y