Question

GIVEN PARALLELOGRAM ABCD, FIND THE LENGTHS AND ANGLES REQUIRED

Answer 1

Co-interior properties. 180 degrees = two co-interior angles.

180 = (2y+50) + (3y+40)
180 = 5y + 90
90 = 5y
/5     /5
18 = y

Angle 1: 2y + 50
              2(18) + 50
              36 + 50
              86

Angle 2: 3y + 40
              3(18) + 40
              54 + 40
              94

86 + 94 = 180 so it is true.

Now the sides.
On a parallelogram, 5x+2 and 8x-7 must be equal

5x + 2 = 8x - 7
        2 = 3x - 7
        9 = 3x
       /3    /3
        3 = x

Side 1: 5x + 2
            5(3) + 2
           15 + 2
           17

Side 2: 8x - 7
            8(3) - 7
            24 - 7
            17

Both sides are equal; 17.

Angle 1: 86
Angle 2: 94
Sides: 17

Answer 2

The measure of the length of the segment AB is 17, the measure of the length of the segment DC is 17, the measure of angle A is 86 degrees, and the measure of angle D is 94 degrees.

Given :

• A parallelogram ABCD.
• The length of the segment AB is (5x + 2).
• The length of the segment DC is (8x - 7).
• Angle A = (2y + 50) degrees
• Angle D = (3y + 40) degrees

The following steps can be used in order to determine the angles and length that are required:

Step 1 - The sum of the two co-interior angles of the parallelogram is 180 degrees.

$\rm \angle A + \angle D = 180^\circ$

(2y + 50) + (3y + 40) = 180

Step 2 - Simplify the above expression.

5y + 70 = 180

5y = 110

y = 18

Step 3 - So, the measure of angle A is:

$\rm \angle A = 2(18) + 50$

$\rm \angle A = 86\;degrees$

Step 4 - Now, the measure of angle D is:

$\rm \angle D = 3(18) + 40$

$\rm \angle D = 94\;degrees$

Step 5 - The opposite sides of a parallelogram are equal in length.

5x + 2 = 8x - 7

3x = 9

x = 3

Step 6 - So, the measure of length AB is:

AB = 5(3) + 2

AB = 17

Step 7 - Now, the measure of length DC is:

DC = 8(3) - 7

DC = 17

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