Question

lines k and l are parallel, and the measure of angle abc is 19°.a. m < ecf=°b. m < bcd=°

Explanation:

Step1: Use the property of alternate - interior angles

Since lines \(k\) and \(l\) are parallel, \(\angle ECF\) and \(\angle ABC\) are alternate - interior angles. By the alternate - interior angles theorem, if two parallel lines are cut by a transversal, then alternate - interior angles are congruent. So \(m\angle ECF=m\angle ABC\). Given \(m\angle ABC = 19^{\circ}\), then \(m\angle ECF=19^{\circ}\).

Step2: Use the property of a straight line

\(\angle ECF+\angle BCD = 180^{\circ}\) (because they form a linear pair, and the sum of angles on a straight line is \(180^{\circ}\)). We know \(m\angle ECF = 19^{\circ}\). Then \(m\angle BCD=180^{\circ}-m\angle ECF\). Substitute \(m\angle ECF = 19^{\circ}\) into the formula: \(m\angle BCD=180 - 19=161^{\circ}\).

Answer:

a. \(19\)
b. \(161\)