Chapter 7.3, Problem 18WE

To determine

To Find: the $m\angle E^{\text{'}}$ in two similar quadrilaterals shown in figure.

Answer to Problem 18WE

  $m\angle E^{\text{'}}={45}^{\circ }$

Explanation of Solution

Given:

Figure is shown as.

  

Calculation:

Since, corresponding angles in two similar polygons are equal.

Therefore, $m\angle T=m\angle T^{\text{'}}=135$ and $m\angle U^{\text{'}}=m\angle N^{\text{'}}=90$

Since, it is a quadrilateral therefore sum of all angles is $360$ .

i.e.,

  $\begin{array}{l}m\angle E^{\text{'}}+m\angle T^{\text{'}}+m\angle U^{\text{'}}+m\angle N^{\text{'}}=360\\ m\angle E^{\text{'}}+135+90+90=360\\ m\angle E^{\text{'}}={45}^{\circ }\end{array}$

Therefore, answer is $m\angle E^{\text{'}}={45}^{\circ }$ .