The given figure is a rectangle.
Given angles are- m∠BDC = 47°, m∠CAB = 52°, and m∠BEC = 99°
The sum of the angles m∠BDC = 47°, m∠CAB = 52° is the measure of m∠BEC which is 99°
This is sufficient to prove. Measure of angle A and D are 90 degrees each as they are right angles triangles. So, inner angle A is 90-52 = 38 degrees. Inner angle D will be 90-47 =43 degrees.
Measure of triangle AED = 180 degrees
Let inner E = x
then, 38+43+x=180
x=99 degrees
Outer E and inner are vertical angles and so, they are same.
Moreover, triangles AED and BEC are same so E is 99 degrees
