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Use KMOQ to find m O .

Q and O are consecutive angles of KMOQ , so they are supplementary. m O + m Q = 180. Definition of supplementary angles. m O + 35 = 180. Substitute 35 for m Q. m O = 145. Subtract 35 from each side. Properties of Parallelograms. LESSON 6-2. Additional Examples.

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Use KMOQ to find m O .

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  1. Q and O are consecutive angles of KMOQ, so they are supplementary. m O + m Q = 180 Definition of supplementary angles m O + 35 = 180 Substitute 35 for m Q. m O = 145 Subtract 35 from each side. Properties of Parallelograms LESSON 6-2 Additional Examples Use KMOQ to find m O. Quick Check

  2. x + 15 = 135 – x Opposite angles of a are congruent. 2x + 15 = 135 Add x to each side. 2x = 120 Subtract 15 from each side. x = 60 Divide each side by 2. Substitute 60 for x. m B = 60 + 15 = 75 m A + m B = 180 Consecutive angles of a parallelogram are supplementary. m A + 75 = 180 Substitute 75 for m B. m A = 105 Subtract 75 from each side. Properties of Parallelograms LESSON 6-2 Additional Examples Quick Check Find the value of x in ABCD. Then find m A.

  3. x = 7y – 16 The diagonals of a parallelogram bisect each other. 2x + 5 = 5y 2(7y – 16) + 5 = 5y Substitute 7y – 16 for x in the second equation to solve for y. 14y – 32 + 5 = 5y Distribute. 14y – 27 = 5y Simplify. –27 = –9y Subtract 14y from each side. 3 = y Divide each side by –9. x = 7(3) – 16 Substitute 3 for y in the first equation to solve for x. x = 5 Simplify. Properties of Parallelograms LESSON 6-2 Additional Examples Find the values of x and y in KLMN. Quick Check So x = 5 and y = 3.

  4. Properties of Parallelograms LESSON 6-2 Additional Examples Theorem 6-4 states If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. Explain how to divide a blank card into five equal rows using Theorem 6-4 and a sheet of lined paper. Place a corner of the top of the card on the first line of the lined paper. Place any other corner on the sixth line. Mark the points where the lines intersect one side of the card. Mark the points where the lines intersect the opposite side of the card. Connect the marks on opposite sides using a straightedge. If you use the same-side bottom corner, the lines are parallel to the top of the card. If you use the opposite corner, the lines are parallel to the diagonal of the card. Quick Check

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