Exercise 28 Page 404

We are given the following polygon.

We are asked to find the measure of angle $AED.$ Let's start by recalling the rule for the sum of the measures of the interior angles of a polygon.

Interior Angle Sum of a Polygon

The sum of the measures of the interior angles of a polygon is $(n-2)180,$ where $n$ represents the number of sides.

To find the sum of the measures of the interior angles of a pentagon, we will substitute $5$ for $n$ in this expression. We got that the sum of the interior angles of a pentagon is $540^{\circ }.$ Note that in the given pentagon, there are three right angles. We also know that angle $AED$ is congruent to angle $BCD.$ This means that these angles have the same measure. Therefore, the polygon has $5$ interior angles, where $3$ angles have the measure of $90^{\circ }$ and $2$ angles have the measure of $x^{\circ }.$ Let's write an equation that represents this situation. Now we can solve this equation for $x.$ For simplicity, we will not write the degree symbol. We got that $x=135.$ This means that the measure of angle $AED$ is equal to $135^{\circ }$ and C is the correct option.