Question

find the measure of ∠bec for rectangle abcd.
the measure of ∠bec is
(type an integer or a decimal. do not include the degree symbol in your answer.)

Explanation:

Step1: Recall properties of rectangle

In rectangle \(ABCD\), \(AE = DE\) (diagonals of a rectangle are equal and bisect each other). So, \(\angle ADE=\angle DAE = 37^{\circ}\).

Step2: Find \(\angle AED\)

Using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)) in \(\triangle ADE\), \(\angle AED=180-(37 + 37)=106^{\circ}\).

Step3: Find \(\angle BEC\)

\(\angle BEC\) and \(\angle AED\) are vertical angles. Vertical angles are equal.

Answer:

\(106\)