Question

2 lines k and l are parallel, and the measure of angle abc is 19°. answer attempt 3 out of 99 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. Alternate - interior angles are equal when two parallel lines are cut by a transversal.
So, \(m\angle ECF=m\angle ABC\)
\(m\angle ECF = 19^{\circ}\)

Step2: Use the property of supplementary angles

We know that \(\angle ECF+\angle FCB+\angle BCD = 180^{\circ}\) (a straight line has an angle measure of \(180^{\circ}\)), and \(\angle FCB = 90^{\circ}\) (right - angle). Also, we found \(m\angle ECF=19^{\circ}\)
Substitute into the equation: \(19^{\circ}+90^{\circ}+m\angle BCD=180^{\circ}\)
\(m\angle BCD=180^{\circ}-(19^{\circ} + 90^{\circ})\)
\(m\angle BCD=71^{\circ}\)

Answer:

a. \(19\)
b. \(71\)