When two adjacent angles add up to 90 degrees (forming a right angle), they are complementary. When two adjacent angles add up to 180 degrees (forming a straight angle, or linear pair), they are supplementary.

Both of the following practice questions contain diagrams. In the first one, you’re shown one angle in a linear pair, and you have to calculate the missing supplementary angle. In the second problem, you’re shown one angle in a right angle, and you have to find its missing complementary angle.## Practice questions

*Use the following diagram to answer the first question.*

- What is the measure of angle
*ABD*?**A.**121 degrees**B.**31 degrees**C.**59 degrees**D.**61 degrees**E.**149 degrees - What is the value of
*x*in the following diagram?**A.**143**B.**53**C.**233**D.**37**E.**63

## Answers and explanations

- The correct answer is Choice
**(C).**Angle ABD and angle*DBC*form a linear pair, so they're supplementary. Therefore, the sum of their measures is 180 degrees. The measure that must be added to 121 degrees is 59 degrees because 180 – 121 = 59. Therefore, the measure of angle*ABD*is 59 degrees. - The correct answer is Choice
**(B).**You can work a problem like this by setting up an algebraic equation. Here, the sum of*x*and 37 must be 90 because the two angles are complementary. They form a right angle together, so the sum of their measures is 90 degrees.