Angle relationships Knowledge-Based Download PDF

Questions

1. 1.

   Ray $OQ$ bisects $\angle POR$, and ray $OS$ is perpendicular to ray $OQ$ such that ray $OR$ lies in the interior of $\angle QOS$. If the measure of $\angle POR$ is $68^\circ$, what is the measure of $\angle ROS$?

   • A) $56^\circ$
   • B) $34^\circ$
   • C) $22^\circ$
   • D) $124^\circ$
2. 2.

   Three straight lines intersect at a single point to form six angles. If three non-adjacent angles among them have measures of $(2x + 10)^\circ$, $(3x - 5)^\circ$, and $(4x + 13)^\circ$, what is the measure of the smallest of these three angles?

   • A) $18^\circ$
   • B) $46^\circ$
   • C) $49^\circ$
   • D) $85^\circ$
3. 3.

   Two straight lines intersect such that a pair of vertical angles have measures of $(5x - 22)^\circ$ and $(3x + 14)^\circ$. What is the measure of an angle that forms a linear pair with one of these vertical angles?

   • A) $112^\circ$
   • B) $68^\circ$
   • C) $122^\circ$
   • D) $54^\circ$
4. 4.

   Two parallel lines are cut by a transversal such that two consecutive interior angles have measures of $(3x + 15)^\circ$ and $(2x + 35)^\circ$. What is the measure of the smaller angle?

   • A) $26^\circ$
   • B) $75^\circ$
   • C) $93^\circ$
   • D) $87^\circ$
5. 5.

   The measure of an angle is $18^\circ$ less than twice the measure of its complement. What is the measure of the supplement of this angle?

   • A) $36^\circ$
   • B) $54^\circ$
   • C) $126^\circ$
   • D) $144^\circ$