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.
