Question

determine $\angle dce$.

Explanation:

Step1: Identify parallel lines and alternate interior angles

Since \( AB \parallel DE \) (implied by the direction of the arrow and the transversal \( AE \)), \( \angle A \) and \( \angle E \) are alternate interior angles. So \( \angle E=\angle A = 35^\circ \).

Step2: Use triangle angle sum property

In \( \triangle DCE \), the sum of interior angles is \( 180^\circ \). Let \( \angle DCE=x \). We know \( \angle D = 53^\circ \) and \( \angle E = 35^\circ \). So, \( x+53^\circ+35^\circ = 180^\circ \).

Step3: Solve for \( x \)

\( x=180^\circ-(53^\circ + 35^\circ)=180^\circ - 88^\circ = 92^\circ \).

Answer:

\( \angle DCE = 92^\circ \)