Question

2 lines ( k ) and ( l ) are parallel, and the measure of angle ( a b c ) is ( 44^{circ} ).
answer attempt 1 out of 99
a. ( m angle e c f=square^{circ} )
b. ( m angle b c d=square^{circ} )

Explanation:

Step1: Use alternate - interior angles

Since lines \(k\) and \(l\) are parallel, \(\angle ECF=\angle ABC\) (alternate - interior angles). Given \(\angle ABC = 49^{\circ}\), so \(m\angle ECF = 49^{\circ}\).

Step2: Use the property of a straight - line angle

We know that \(\angle ECF+\angle BCD+\angle FCB = 180^{\circ}\), and \(\angle FCB=\angle ABC = 49^{\circ}\) (vertical angles are equal). Also, \(\angle ECF = 49^{\circ}\). Then \(m\angle BCD=180^{\circ}-49^{\circ}-49^{\circ}\).

$$m\angle BCD = 82^{\circ}$$

Answer:

a. \(49\)
b. \(82\)