Parallel and perpendicular lines Knowledge-Based Download PDF

Questions

1. 1.

   In a plane, line $l_1$ is parallel to line $l_2$, and line $l_2$ is perpendicular to line $l_3$. If line $l_4$ intersects line $l_1$ at an acute angle of $31^\circ$, what is the measure of the acute angle formed by line $l_4$ and line $l_3$?

   • A) $31^\circ$
   • B) $49^\circ$
   • C) $59^\circ$
   • D) $69^\circ$
2. 2.

   In a plane, two parallel lines are intersected by a transversal. What is the measure of the angle formed by the intersection of the bisectors of two consecutive interior angles?

   • A) 45°
   • B) 60°
   • C) 75°
   • D) 90°
3. 3.

   In a plane, line $l$ is parallel to line $m$, and a transversal intersects line $l$ at $A$ and line $m$ at $B$. If segment $AC$ is perpendicular to line $m$ at point $C$ and $\angle BAC = 34^\circ$, what is the measure of the obtuse angle formed by the transversal and line $l$ at point $A$?

   • A) 112°
   • B) 118°
   • C) 124°
   • D) 146°
4. 4.

   Two coplanar lines are intersected by a transversal such that a pair of consecutive interior angles measure $(3x + 15)^\circ$ and $(2x + 35)^\circ$. What value of $x$ ensures that the two lines are parallel?

   • A) 26
   • B) 20
   • C) 8
   • D) 36
5. 5.

   In a plane, lines $L_1$ and $L_2$ are both perpendicular to line $L_3$. If line $L_4$ is perpendicular to line $L_1$, which statement must be true regarding lines $L_2$ and $L_4$?

   • A) Line $L_2$ is parallel to line $L_4$.
   • B) Line $L_2$ and line $L_4$ intersect at an acute angle of $45^\circ$.
   • C) Line $L_2$ is perpendicular to line $L_4$.
   • D) Line $L_2$ and line $L_4$ do not intersect and are skew lines.