Chapter 5.4, Problem 11WE

To determine

To find: The angles 2, 3, 4 and 5.

Answer to Problem 11WE

The angles 2, 3, 4 and 5 are 25, 65, 65 and 90.

Explanation of Solution

Given:

The rhombus is shown below:

  

The angle 1 is 25.

Calculation:

Diagonals of rhombus are perpendicular to each other.

  $m\angle 5=90$

Diagonal of rhombus bisect the vertex angle.

Hence,

  $m\angle 1=m\angle 2=25$

Sum of angle S and L is supplementary.

Hence,

  $\begin{array}{l}m\angle S+m\angle L=180°\\ m\angle 1+m\angle 2+m\angle 3+m\angle 4=180\\ 25+25+m\angle 3+m\angle 3=180\\ 2m\angle 3=130\\ m\angle 3=65\end{array}$

And,

  $m\angle 3=m\angle 4=65$

Thus, the angles 2, 3, 4 and 5 are 25, 65, 65 and 90.