Chapter 5.4, Problem 14WE

To determine

To find: The angles 2, 3 and 4.

Answer to Problem 14WE

The angles 2, 3 and 4 are 18, 72 and 72.

Explanation of Solution

Given:

The rectangle is shown below:

  

The angle 1 is $18$ .

Calculation:

As the diagonal of rectangle bisect each other and equal to each other as well, the sides OT and OA are equal.

Hence,

  $m\angle 1=m\angle 2\left(\text{Opposite}\text{}\text{angles}\text{of}\text{sides}\right)$

Thus, the angle 2 is,

  $m\angle 2=\text{18}$

Sum of angles 2 and 3 is complementary as angle of rectangle.

  $\begin{array}{l}m\angle 2+m\angle 3=90\\ 18+m\angle 3=90\\ m\angle 3=72\end{array}$

Also,

As the diagonal of rectangle bisect each other and equal to each other as well, the sides OA and OL are equal.

Hence,

  $m\angle 3=m\angle 4=72\left(\text{Opposite}\text{}\text{angles}\text{of}\text{sides}\right)$

Thus, the angles 2, 3 and 4 are 18, 72 and 72.