Chapter 6.4, Problem 12PPS

To determine

The measure of angle DEB.

Answer to Problem 12PPS

  $m\angle DEB=90°$

Explanation of Solution

Given:

The given figure is:

  $AB=6\text{ feet, AC = 2 feet and m}\angle \text{CAE = 65}\text{.}$

Calculation:

The opposite sides of rectangle are equal in length and there are 4 right angles.

The diagonals of a rectangle are perpendicular and bisect the angles at the vertex.

In given figure, triangle DEB is right triangle and is also isosceles triangle, as the diagonals bisect one another.

Hence,

  $m\angle DEB=90°$