Section 12.1: Adjacent and Vertical Angles — Practice Questions

1. 1. Two straight lines intersect. One of the angles formed measures $85$°. What is the degree measure of its vertically opposite angle? ___

2. 2. Two vertical angles have measures of $95$° and $(5x + 15)$°. What is the value of $x$? ___

3. 3. When two straight lines intersect, which statement is always true about the angles that are vertically opposite each other?

   • A. They are supplementary (add up to 180°).
   • B. They are congruent (have the same measure).
   • C. They are complementary (add up to 90°).
   • D. One is always twice the measure of the other.

4. 4. Two vertical angles have measures given by the expressions $(7x - 10)$° and $(4x + 11)$°. Find the value of $x$. ___

5. 5. Two vertical angles measure $(2y + 5)$° and $(4y - 25)$°. What is the actual degree measure of each of these angles? ___

6. 6. Two adjacent angles, $\angle PQR$ and $\angle RQS$, form the larger angle $\angle PQS$. If $m\angle PQR = 55^\circ$ and $m\angle RQS = 30^\circ$, what is the measure of $\angle PQS$ in degrees? ___

7. 7. Two adjacent angles form a straight line, which measures $180^\circ$. If one angle measures $72^\circ$, what is the measure of the other angle?

   • A. $18^\circ$
   • B. $72^\circ$
   • C. $108^\circ$
   • D. $252^\circ$

8. 8. Two adjacent angles form a right angle ($90^\circ$). The measures of the angles are $(4x + 8)^\circ$ and $(2x + 4)^\circ$. Find the value of $x$. ___

9. 9. Which of the following must be true for two angles to be considered adjacent?

   • A. They must both be acute angles.
   • B. Their sum must be exactly $180^\circ$.
   • C. They must share a common vertex and a common side.
   • D. They must be equal in measure.

10. 10. Two adjacent angles form a straight angle ($180^\circ$). Their measures are $(5x + 15)^\circ$ and $(x + 3)^\circ$. What is the value of $x$? ___