Question

1. in the diagram, line ( l ) is parallel to line ( m ) and cut by transversals ( s ) and ( t ).

what is the measure of ( angle 1 )?
a. ( 42^{circ} )
b. ( 61^{circ} )
c. ( 119^{circ} )
d. ( 103^{circ} )

Explanation:

Step1: Find the measure of the angle adjacent to \(138^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the angle adjacent to \(138^{\circ}\) is \(180^{\circ}- 138^{\circ}=42^{\circ}\)

Step2: Use the property of parallel lines and transversals (sum of angles in a triangle - like situation)

We know that the sum of angles around the intersection of transversals \(s\) and \(t\) with line \(l\) should follow the angle - sum property. Let's consider the angles formed. The sum of angles around the intersection point: we have a \(77^{\circ}\) angle, the \(42^{\circ}\) angle (from Step 1) and \(\angle1\). Using the fact that the sum of angles around a point (in this case, related to the parallel - line transversal intersection) is such that \(\angle1=180^{\circ}-(77^{\circ}+42^{\circ})\)

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Answer:

B. \(61^{\circ}\)