Question

find ( mangle bec ).
( mangle bec=square^{circ} )

Explanation:

Step1: Identify the right angle

We know that \(\angle AEB = 90^{\circ}\) (given as a right - angle). Also, \(\angle AEB+\angle BEC+\angle CED = 180^{\circ}\) (since \(AED\) is a straight line, and the sum of angles on a straight line is \(180^{\circ}\)).

Step2: Use the angle - sum relationship

We can rewrite the equation as \(m\angle BEC=90^{\circ}-m\angle CED\) (because \(\angle AEB = 90^{\circ}\) and \(m\angle AEB + m\angle BEC+m\angle CED=180^{\circ}\), so \(m\angle BEC=180^{\circ}-\angle AEB - m\angle CED\), substituting \(\angle AEB = 90^{\circ}\)).

Given \(m\angle CED = 48^{\circ}\), then \(m\angle BEC=90^{\circ}-48^{\circ}\)

$$m\angle BEC = 42^{\circ}$$

Answer:

\(42\)