FIND MISSING ANGLES AND SIDES OF TRAPEZIUM

What is trapezium ?

A trapezium is a quadrilateral which has a pair of parallel opposite sides.

Properties :

• A trapezium has two parallel sides and two non parallel sides.
• The diagonal of regular trapezium bisect each other.
• The length of the midsegment is equal to half the sum of parallel bases.
• Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non parallel side, add up to 180 degrees.

Find the values of the variables. Then find the lengths of the sides.

Problem 1 :

Solution :

By observing the figure,

4y + 6 = 7y – 3

Comparing like terms.

4y – 7y = -3 – 6

-3y = -9

y = 3

To find the lengths of the sides :

Substitute y = 3 in 4y + 6

= 4(3) + 6

= 12 + 6

= 18

Base of the trapezium = 5y + 1.4

5(3) + 1.4

15 + 1.4

16.4

So, the lengths of the sides are 18, 18, 16.4, 4.8.

Problem 2 :

The figure is an isosceles trapezoid. Determine the value of the variable

a) x = 3     b) x = 2      c) x = 18x + 48      d) x = 51

Solution :

17x = x + 48

Subtract x from both sides.

17x – x = x – x + 48

16x = 48

Divide both sides by 16.

16x/16 = 48/16

x = 3

So, the value is x = 3.

Problem 3 :

Find the value of x in the trapezium ABCD given below.

Solution :

Sum of co interior angles = 180

x - 20 + x + 40 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

Problem 4 :

Find the value of y, if the perimeter of the trapezium is 142.

Solution :

y + 12 + y + 12 + y + y - 12 = 164

4y + 12 = 164

4y = 164 - 12

4y = 152

y = 152/4

y = 38