[tex]m\angle D\text{ = }26[/tex]
Here, we want to calculate the measure of angle D
Firstly, we can calculate the measure of angle A
Since BE and AD are perpendicular, it follws that triangle ABE is a right angled triangle
Thus,
52 + A = 90
A = 90-52
A = 38
Now, from the question, we are told that EBD and CBD are congruent, meaning that they are equal
We can deduce from the diagarm that;
[tex]\angle ABE\text{ + }\angle CBD\text{ + }\angle EBD\text{ = 180}[/tex]
The reason for this is that they are all on a straight line and the measure of angles on a straight line is 180
Thus, since we have the two angles equal, then;
[tex]\begin{gathered} \angle EBD\text{ = }\frac{180-52}{2} \\ \\ \angle EBD\text{ = 64} \end{gathered}[/tex]
The measure of angle B in triangle ABD would be 64 + 52 = 116.
Since we have two angles out of triangle ABD, we can get the measure of the third angle which is angle D (Sum of angles in a triangle = 180)
Mathematically, that would be;
[tex]\begin{gathered} \angle D\text{ + 116 + 38 = 180} \\ \angle D\text{ = 180-116-38} \\ \\ \angle D\text{ = 26} \end{gathered}[/tex]
