Question

what is ( mangle2 + mangle3 )?

Explanation:

Step1: Determine the relationship between the lines

Since \(AB\parallel CD\) (the two lines are drawn as parallel with arrows indicating direction), and \(AC\) is perpendicular to the parallel lines (as shown by the right - angle symbols).

Step2: Use the property of parallel lines and transversal

By the property of parallel lines, the alternate - interior angles are equal. So \(\angle2=\angle4\).

Step3: Consider the sum of angles

We know that \(\angle3+\angle4 = 90^{\circ}\) (because \(AC\) is perpendicular to the parallel lines, forming a right - angle at \(C\)).
Since \(\angle2=\angle4\), then \(m\angle2 + m\angle3=m\angle4 + m\angle3\).

Answer:

\(90\)