Question

in the figure above ( a parallel b ). if ( angle 1 = 34 ), find the measure of ( angle 2 )
a 56
b 34
c 146
d 90

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines \(a\parallel b\) are cut by a transversal, the alternate - interior angles are equal.
\(\angle1\) and \(\angle2\) are alternate - interior angles.

Step2: Find the measure of \(\angle2\)

Since \(a\parallel b\) and \(\angle1 = 34^{\circ}\), by the alternate - interior angles theorem, \(\angle2=\angle1\).

Answer:

\(34\) (corresponding to option B)