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= 19° b. m < bcd= °

Explanation:

Step1: Use the property of parallel lines and alternate - interior angles

Since lines \(k\) and \(l\) are parallel, \(\angle ECF\) and \(\angle ABC\) are alternate - interior angles. So \(\angle ECF=\angle ABC = 19^{\circ}\) (given in part a).

Step2: Use the straight - line angle property

We know that \(\angle ECF+\angle FCD+\angle BCD = 180^{\circ}\) (a straight line has an angle measure of \(180^{\circ}\)). Also, \(\angle FCD\) and \(\angle ABC\) are alternate - interior angles (because \(k\parallel l\)), so \(\angle FCD=\angle ABC = 19^{\circ}\).
Substitute \(\angle ECF = 19^{\circ}\) and \(\angle FCD=19^{\circ}\) into the equation \(\angle ECF+\angle FCD+\angle BCD = 180^{\circ}\).
We get \(19^{\circ}+19^{\circ}+\angle BCD=180^{\circ}\).

Step3: Solve for \(\angle BCD\)

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Answer:

\(142\)