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Question

1. Two opposite angles of a parallelogram measure (5x-25) degrees and (3x+5) degrees. find the measures of the angles. 

2. Parallelogram JKLM has vertices j(0,7) K(9,7) and L(6,0). Find the coordinates of M. 

Answer 1

1.

The two opposite angles are ( 5x - 25 ) degrees and ( 3x + 5 ) degrees.

In a parallelogram opposite angles are congruent.

So , 5 x - 25 = 3x + 5

=>5x - 3x = 5 +25

=> 2x = 30

Hence x = 15.

Now  (5 x -25 ) = [ 5(15) - 25] = 75 - 25 = 50 º

          (3 x +5 ) [ 3 (15) + 5] = 45 + 5 = 50º

Hence the angles  measure 50º .

Answer 2

2.

Parallelogram JKLM has vertices J(0,7) K(9,7) and L(6,0) .

Let the fourth vertex M be (x , y) .

The two diagnoals of the paralleogram should bisect each other .

So ,the midpoint of  JL = midpoint of KM

[ ( 0 + 6 ) / 2 , ( 7 + 0) / 2 ] = [ (9 + x) / 2 ,(7 + y) / 2]

[ 3 , 7 / 2] = [(9 + x) / 2 ,(7 + y) /2]

( 9 + x ) / 2 = 3   

9 + x = 6

x  =  - 3 .

( 7 + y )/ 2  = 7 / 2

7 + y = 7

y = 0.

So, the coordinates of M (x , y) are ( - 3 , 0 ) .