Question

2 lines k and l are parallel, and the measure of angle abc is 19°. answer attempt 5 out of 99 a. m < ecf = a° b. m < bcd = °

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Since angle \(ECF\) and angle \(BCA\) are vertical angles, and angle \(ABC = 19^{\circ}\), and lines \(k\) and \(l\) are parallel, so \(m\angle ECF=m\angle ABC = 19^{\circ}\) (alternate - interior angles are equal when two parallel lines are cut by a transversal).

Step2: Use the property of a straight - line angle

The sum of angles on a straight line is \(180^{\circ}\). We know that \(\angle ECF+\angle BCD = 180^{\circ}\) (linear pair). Since \(m\angle ECF = 19^{\circ}\), then \(m\angle BCD=180^{\circ}-m\angle ECF\).

Answer:

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