Chapter 6.4, Problem 9WE

To determine

To find: the largest angle

Answer to Problem 9WE

Angle numbered 3 is the largest

Explanation of Solution

Formula used:

Angle opposite to the larger side is greater than the angle opposite to the shorter side.

Calculation:

  

In the quadrilateral ABCD,

  $AB\parallel CD,AD\parallel BC$ (Given)

So, ABCD is a parallelogram.

(A quadrilateral in which opposite sides are parallel is a parallelogram)

As ABCD is a parallelogram,

  $DC=AB=22$ (opposite sides of a parallelogram are equal)

In $\Delta BCD$ ,

  $BD=21,BC=20,CD=22$

In $\Delta BCD$ ,

  $BC<BD<CD$

CD is the longest side

Angle opposite to side CD is $\angle B$ which is numbered as 3 in the figure.

So, Angle numbered 3 is the largest