Parallel and perpendicular lines Knowledge-Based Practice

Questions

1. 1.

   In a plane, two parallel lines are intersected by a transversal. If the angle bisectors of two consecutive interior angles intersect at point $P$, what is the measure of the angle formed by these two bisectors at point $P$?

   • A) $90^\circ$
   • B) $45^\circ$
   • C) $60^\circ$
   • D) $120^\circ$
2. 2.

   In a plane, lines $p$ and $q$ are parallel, and a transversal line $t$ intersects line $p$ at an acute angle of $50^\circ$. If line $s$ is perpendicular to transversal $t$ at its point of intersection with line $q$, what is the measure of the acute angle formed between line $s$ and line $q$?

   • A) $30^\circ$
   • B) $50^\circ$
   • C) $60^\circ$
   • D) $40^\circ$
3. 3.

   Two parallel lines are intersected by a transversal line. If the measures of two consecutive interior angles are in the ratio $2 : 3$, what is the measure of the smaller angle?

   • A) $36^\circ$
   • B) $72^\circ$
   • C) $108^\circ$
   • D) $144^\circ$
4. 4.

   In a plane, two distinct lines are intersected by a transversal. Which of the following conditions is sufficient to prove that the two lines are parallel?

   • A) A pair of vertical angles are congruent.
   • B) A pair of alternate interior angles are congruent.
   • C) A pair of consecutive interior angles are complementary.
   • D) A pair of adjacent angles are supplementary.
5. 5.

   In a plane, line $k$ is perpendicular to line $m$, and line $m$ is parallel to line $n$. Which of the following statements must be true regarding lines $k$ and $n$?

   • A) Line $k$ is parallel to line $n$.
   • B) Line $k$ coincides with line $n$.
   • C) Line $k$ is perpendicular to line $n$.
   • D) Line $k$ and line $n$ do not intersect.

Answers and step-by-step solutions appear after you finish the test.