Question

question #14
lines fd and ge are parallel in the figure below.
if ( mangle bac = 65^{circ} ), what is ( mangle abc )?
a ( 30^{circ} )
b ( 65^{circ} )
c ( 85^{circ} )
d ( 105^{circ} )

Explanation:

Step1: Use the property of parallel lines

Since \(FD\parallel GE\), we can use the alternate - interior angles property. Let's assume the line \(BC\) is a transversal.

Step2: Analyze the angles

We know that \(\angle BAC = 65^{\circ}\) and there is a \(30^{\circ}\) angle. The sum of angles formed by a transversal with parallel lines: \(\angle ABC=\angle BAC + 30^{\circ}\) (by the property of alternate - interior angles and angle addition).

Step3: Calculate \(\angle ABC\)

\(\angle ABC=65^{\circ}+ 40^{\circ}=105^{\circ}\)

Answer:

D. \(105^{\circ}\)