Given that m∠bdc = 47°, m∠cab = 52°, and m∠bec = 99° is there enough evidence to prove that . if so, explain. (3 points)

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