Question

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

Explanation:

Step1: Use rectangle diagonal property

In rectangle \(ABCD\), diagonals bisect each other, so \(AE = DE\). Thus, \(\triangle AED\) is isosceles, so \(\angle ADE = \angle DAE = 34^\circ\).

Step2: Calculate \(\angle AED\)

Sum of angles in a triangle is \(180^\circ\).
\(\angle AED = 180^\circ - 34^\circ - 34^\circ = 112^\circ\)

Step3: Relate \(\angle AED\) to \(\angle BEC\)

Vertical angles are equal, so \(\angle BEC = \angle AED\).

Answer:

112