Parallel lines and transversals Knowledge-Based Download PDF

Questions

1. 1.

   Two parallel lines are intersected by a transversal. The sum of the degree measures of two alternate interior angles is equal to the degree measure of an obtuse angle formed by these lines and the transversal. What is the degree measure of each acute angle formed at these intersections?

   • A) $45^\circ$
   • B) $60^\circ$
   • C) $75^\circ$
   • D) $120^\circ$
2. 2.

   Two parallel lines are intersected by a transversal, forming a pair of consecutive exterior angles with measures of $(7x + 12)^\circ$ and $(3x + 28)^\circ$. What is the degree measure of the larger of these two angles?

   • A) $110^\circ$
   • B) $70^\circ$
   • C) $98^\circ$
   • D) $40^\circ$
3. 3.

   Two parallel lines are intersected by a transversal. If the measure of an obtuse angle formed at one intersection is $24^\circ$ greater than three times the measure of an acute angle formed at the other intersection, what is the degree measure of the obtuse angle?

   • A) $126^\circ$
   • B) $141^\circ$
   • C) $147^\circ$
   • D) $156^\circ$
4. 4.

   Two parallel lines are intersected by a transversal, forming a pair of alternate interior angles with measures of $(5x - 18)^\circ$ and $(3x + 14)^\circ$. What is the degree measure of an angle that forms a linear pair with either of these alternate interior angles?

   • A) 62°
   • B) 108°
   • C) 118°
   • D) 128°
5. 5.

   Two parallel lines are intersected by a transversal such that two consecutive interior angles have measures of $(3x + 10)^\circ$ and $(2x + 45)^\circ$. What is the degree measure of the smaller angle?

   • A) $25^\circ$
   • B) $75^\circ$
   • C) $85^\circ$
   • D) $95^\circ$